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# RD Sharma solutions for Class 11 Mathematics Textbook chapter 33 - Probability [Latest edition]

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## Chapter 33: Probability

Exercise 33.1Exercise 33.2Exercise 33.3Exercise 33.4Others
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Exercise 33.1[Pages 6 - 7]

### RD Sharma solutions for Class 11 Mathematics Textbook Chapter 33 ProbabilityExercise 33.1[Pages 6 - 7]

Exercise 33.1 | Q 1 | Page 6

A coin is tossed once. Write its sample space

Exercise 33.1 | Q 2 | Page 6

If a coin is tossed two times, describe the sample space associated to this experiment.

Exercise 33.1 | Q 3 | Page 6

If a coin is tossed three times (or three coins are tossed together), then describe the sample space for this experiment.

Exercise 33.1 | Q 4 | Page 6

Write the sample space for the experiment of tossing a coin four times.

Exercise 33.1 | Q 5 | Page 6

Two dice are thrown. Describe the sample space of this experiment.

Exercise 33.1 | Q 6 | Page 6

What is the total number of elementary events associated to the random experiment of throwing three dice together?

Exercise 33.1 | Q 7 | Page 6

A coin is tossed and then a die is thrown. Describe the sample space for this experiment.

Exercise 33.1 | Q 8 | Page 6

A coin is tossed and then a die is rolled only in case a head is shown on the coin. Describe the sample space for this experiment.

Exercise 33.1 | Q 9 | Page 6

A coin is tossed twice. If the second throw results in a tail, a die is thrown. Describe the sample space for this experiment.

Exercise 33.1 | Q 10 | Page 6

An experiment consists of tossing a coin and then tossing it second time if head occurs. If a tail occurs on the first toss, then a die is tossed once. Find the sample space.

Exercise 33.1 | Q 11 | Page 7

A coin is tossed. If it shows tail, we draw a ball from a box which contains 2 red 3 black balls; if it shows head, we throw a die. Find the sample space of this experiment.

Exercise 33.1 | Q 12 | Page 7

A coin is tossed repeatedly until a tail comes up for the first time. Write the sample space for this experiment.

Exercise 33.1 | Q 13 | Page 7

A box contains 1 red and 3 black balls. Two balls are drawn at random in succession without replacement. Write the sample space for this experiment.

Exercise 33.1 | Q 14 | Page 7

A pair of dice is rolled. If the outcome is a doublet, a coin is tossed. Determine the total number of elementary events associated to this experiment.

Exercise 33.1 | Q 15 | Page 7

A coin is tossed twice. If the second draw results in a head, a die is rolled. Write the sample space for this experiment.

Exercise 33.1 | Q 16 | Page 7

A bag contains 4 identical red balls and 3 identical black balls. The experiment consists of drawing one ball, then putting it into the bag and again drawing a ball. What are the possible outcomes of the experiment?

Exercise 33.1 | Q 17 | Page 7

In a random sampling three items are selected from a lot. Each item is tested and classified as defective (D) or non-defective (N). Write the sample space of this experiment.

Exercise 33.1 | Q 18.1 | Page 7

An experiment consists of boy-girl composition of families with 2 children.

What is the sample space if we are interested in knowing whether it is a boy or girl in the order of their births?

Exercise 33.1 | Q 18.2 | Page 7

An experiment consists of boy-girl composition of families with 2 children.

What is the sample space if we are interested in the number of boys in a family?

Exercise 33.1 | Q 19 | Page 7

There are three coloured dice of red, white and black colour. These dice are placed in a bag. One die is drawn at random from the bag and rolled its colour and the number on its uppermost face is noted. Describe the sample space for this experiment.

Exercise 33.1 | Q 20 | Page 7

2 boys and 2 girls are in room P and 1 boy 3 girls are in room Q. Write the sample space for the experiment in which a room is selected and then a person.

Exercise 33.1 | Q 21 | Page 7

A bag contains one white and one red ball. A ball is drawn from the bag. If the ball drawn is white it is replaced in the bag and again a ball is drawn. Otherwise, a die is tossed. Write the sample space for this experiment.

Exercise 33.1 | Q 22 | Page 7

A box contains 1 white and 3 identical black balls. Two balls are drawn at random in succession without replacement. Write the sample space for this experiment.

Exercise 33.1 | Q 23 | Page 7

An experiment consists of rolling a die and then tossing a coin once if the number on the die is even. If the number on the die is odd, the coin is tossed twice. Write the sample space for this experiment.

Exercise 33.1 | Q 24 | Page 7

A die is thrown repeatedly until a six comes up. What is the sample space for this experiment.

Exercise 33.2[Pages 15 - 16]

### RD Sharma solutions for Class 11 Mathematics Textbook Chapter 33 ProbabilityExercise 33.2[Pages 15 - 16]

Exercise 33.2 | Q 1 | Page 15

A coin is tossed. Find the total number of elementary events and also the total number events associated with the random experiment.

Exercise 33.2 | Q 2 | Page 15

List all events associated with the random experiment of tossing of two coins. How many of them are elementary events.

Exercise 33.2 | Q 3.1 | Page 15

Three coins are tossed once. Describe the events associated with this random experiment:

A = Getting three heads
B = Getting two heads and one tail
C = Getting three tails
D = Getting a head on the first coin.
(i) Which pairs of events are mutually exclusive?

Exercise 33.2 | Q 3.2 | Page 15

Three coins are tossed once. Describe the events associated with this random experiment:

A = Getting three heads
B = Getting two heads and one tail
C = Getting three tails
D = Getting a head on the first coin.

(ii) Which events are elementary events?

Exercise 33.2 | Q 3.3 | Page 15

Three coins are tossed once. Describe the events associated with this random experiment:

A = Getting three heads
B = Getting two heads and one tail
C = Getting three tails
D = Getting a head on the first coin.

(iii) Which events are compound events?

Exercise 33.2 | Q 4.1 | Page 15

In a single throw of a die describe the event:

A = Getting a number less than 7

Exercise 33.2 | Q 4.2 | Page 15

In a single throw of a die describe the event:

B = Getting a number greater than 7

Exercise 33.2 | Q 4.3 | Page 15

In a single throw of a die describe the event:

C = Getting a multiple of 3

Exercise 33.2 | Q 4.4 | Page 15

In a single throw of a die describe the event:

D = Getting a number less than 4

Exercise 33.2 | Q 4.5 | Page 15

In a single throw of a die describe the event:

E = Getting an even number greater than 4

Exercise 33.2 | Q 4.6 | Page 15

In a single throw of a die describe the event:

F = Getting a number not less than 3.
Also, find A ∪ BA ∩ BB ∩ CE ∩ FD ∩ F and $\bar { F }$ .

Exercise 33.2 | Q 5.1 | Page 15

Three coins are tossed. Describe.  two events A and B which are mutually exclusive.

Exercise 33.2 | Q 5.2 | Page 15

Three coins are tossed. Describe. three events AB and C which are mutually exclusive and exhaustive.

Exercise 33.2 | Q 5.3 | Page 15

Three coins are tossed. Describe. two events A and B which are not mutually exclusive.

Exercise 33.2 | Q 5.4 | Page 15

Three coins are tossed. Describe.

(iv) two events A and B which are mutually exclusive but not exhaustive.

Exercise 33.2 | Q 6 | Page 16

A die is thrown twice. Each time the number appearing on it is recorded. Describe the following events:

A = Both numbers are odd.
B = Both numbers are even.
C = sum of the numbers is less than 6
Also, find A ∪ BA ∩ BA ∪ CA ∩ C
Which pairs of events are mutually exclusive?

Exercise 33.2 | Q 7.1 | Page 16

Two dice are thrown. The events ABCDE and F are described as :
A = Getting an even number on the first die.
B = Getting an odd number on the first die.
C = Getting at most 5 as sum of the numbers on the two dice.
D = Getting the sum of the numbers on the dice greater than 5 but less than 10.
E = Getting at least 10 as the sum of the numbers on the dice.
F = Getting an odd number on one of the dice.
Describe the event:
A and BB or CB and CA and EA or FA and F

Exercise 33.2 | Q 7.2 | Page 16

Two dice are thrown. The events ABCDE and F are described as :
A = Getting an even number on the first die.
B = Getting an odd number on the first die.
C = Getting at most 5 as sum of the numbers on the two dice.
D = Getting the sum of the numbers on the dice greater than 5 but less than 10.
E = Getting at least 10 as the sum of the numbers on the dice.
F = Getting an odd number on one of the dice.

State true or false:
(a) A and B are mutually exclusive.
(b) A and B are mutually exclusive and exhaustive events.
(c) A and C are mutually exclusive events.
(d) C and D are mutually exclusive and exhaustive events.
(e) CD and E are mutually exclusive and exhaustive events.
(f) A' and B' are mutually exclusive events.
(g) ABF are mutually exclusive and exhaustive events.

Exercise 33.2 | Q 8 | Page 16

The numbers 1, 2, 3 and 4 are written separately on four slips of paper. The slips are then put in a box and mixed thoroughly. A person draws two slips from the box, one after the other, without replacement. Describe the following events:
A = The number on the first slip is larger than the one on the second slip.
B = The number on the second slip is greater than 2
C = The sum of the numbers on the two slips is 6 or 7
D = The number on the second slips is twice that on the first slip.
Which pair(s) of events is (are) mutually exclusive?

Exercise 33.2 | Q 9.1 | Page 16

A card is picked up from a deck of 52 playing cards.

What is the sample space of the experiment?

Exercise 33.2 | Q 9.2 | Page 16

A card is picked up from a deck of 52 playing cards.

What is the event that the chosen card is a black faced card?

Exercise 33.3[Pages 45 - 48]

### RD Sharma solutions for Class 11 Mathematics Textbook Chapter 33 ProbabilityExercise 33.3[Pages 45 - 48]

Exercise 33.3 | Q 1.1 | Page 45

A dice is thrown. Find the probability of getting a prime number

Exercise 33.3 | Q 1.2 | Page 45

A dice is thrown. Find the probability of getting:

2 or 4

Exercise 33.3 | Q 1.3 | Page 45

A dice is thrown. Find the probability of getting a multiple of 2 or 3.

Exercise 33.3 | Q 2.01 | Page 45

In a simultaneous throw of a pair of dice, find the probability of getting:

8 as the sum

Exercise 33.3 | Q 2.02 | Page 45

In a simultaneous throw of a pair of dice, find the probability of getting a doublet

Exercise 33.3 | Q 2.03 | Page 45

In a simultaneous throw of a pair of dice, find the probability of getting a doublet of prime numbers

Exercise 33.3 | Q 2.04 | Page 45

In a simultaneous throw of a pair of dice, find the probability of getting a doublet of odd numbers

Exercise 33.3 | Q 2.05 | Page 45

In a simultaneous throw of a pair of dice, find the probability of getting a sum greater than 9

Exercise 33.3 | Q 2.06 | Page 45

In a simultaneous throw of a pair of dice, find the probability of getting  an even number on first

Exercise 33.3 | Q 2.07 | Page 45

In a simultaneous throw of a pair of dice, find the probability of getting an even number on one and a multiple of 3 on the other

Exercise 33.3 | Q 2.08 | Page 45

In a simultaneous throw of a pair of dice, find the probability of getting neither 9 nor 11 as the sum of the numbers on the faces

Exercise 33.3 | Q 2.09 | Page 45

In a simultaneous throw of a pair of dice, find the probability of getting a sum more than 6

Exercise 33.3 | Q 2.1 | Page 45

In a simultaneous throw of a pair of dice, find the probability of getting a sum less than 7

Exercise 33.3 | Q 2.11 | Page 45

In a simultaneous throw of a pair of dice, find the probability of getting a sum more than 7

Exercise 33.3 | Q 2.12 | Page 45

In a simultaneous throw of a pair of dice, find the probability of getting neither a doublet nor a total of 10

Exercise 33.3 | Q 2.13 | Page 45

In a simultaneous throw of a pair of dice, find the probability of getting odd number on the first and 6 on the second

Exercise 33.3 | Q 2.14 | Page 45

In a simultaneous throw of a pair of dice, find the probability of getting a number greater than 4 on each die

Exercise 33.3 | Q 2.15 | Page 45

In a simultaneous throw of a pair of dice, find the probability of getting a total of 9 or 11

Exercise 33.3 | Q 2.16 | Page 45

In a simultaneous throw of a pair of dice, find the probability of getting a total greater than 8.

Exercise 33.3 | Q 3 | Page 45

In a single throw of three dice, find the probability of getting a total of 17 or 18.

Exercise 33.3 | Q 4.1 | Page 46

Three coins are tossed together. Find the probability of getting exactly two heads

Exercise 33.3 | Q 4.2 | Page 46

Three coins are tossed together. Find the probability of getting at least two heads

Exercise 33.3 | Q 4.3 | Page 46

Three coins are tossed together. Find the probability of getting at least one head and one tail.

Exercise 33.3 | Q 5 | Page 46

What is the probability that an ordinary year has 53 Sundays?

Exercise 33.3 | Q 6 | Page 46

What is the probability that a leap year has 53 Sundays and 53 Mondays?

Exercise 33.3 | Q 7 | Page 46

A and B throw a pair of dice. If A throws 9, find B's chance of throwing a higher number.

Exercise 33.3 | Q 9 | Page 46

Two unbiased dice are thrown. Find the probability that the total of the numbers on the dice is greater than 10.

Exercise 33.3 | Q 10.01 | Page 46

A card is drawn at random from a pack of 52 cards. Find the probability that the card drawn is a black king

Exercise 33.3 | Q 10.02 | Page 46

A card is drawn at random from a pack of 52 cards. Find the probability that the card drawn is either a black card or a king

Exercise 33.3 | Q 10.03 | Page 46

A card is drawn at random from a pack of 52 cards. Find the probability that the card drawn is black and a king

Exercise 33.3 | Q 10.04 | Page 46

A card is drawn at random from a pack of 52 cards. Find the probability that the card drawn is a jack, queen or a king

Exercise 33.3 | Q 10.05 | Page 46

A card is drawn at random from a pack of 52 cards. Find the probability that the card drawn is neither a heart nor a king

Exercise 33.3 | Q 10.06 | Page 46

A card is drawn at random from a pack of 52 cards. Find the probability that the card drawn is spade or an ace

Exercise 33.3 | Q 10.07 | Page 46

A card is drawn at random from a pack of 52 cards. Find the probability that the card drawn is  neither an ace nor a king

Exercise 33.3 | Q 10.08 | Page 46

A card is drawn at random from a pack of 52 cards. Find the probability that the card drawn is a diamond card

Exercise 33.3 | Q 10.09 | Page 46

A card is drawn at random from a pack of 52 cards. Find the probability that the card drawn is not a diamond card

Exercise 33.3 | Q 10.1 | Page 46

A card is drawn at random from a pack of 52 cards. Find the probability that the card drawn is a black card

Exercise 33.3 | Q 10.11 | Page 46

A card is drawn at random from a pack of 52 cards. Find the probability that the card drawn is not an ace

Exercise 33.3 | Q 10.12 | Page 46

A card is drawn at random from a pack of 52 cards. Find the probability that the card drawn is not a black card.

Exercise 33.3 | Q 11 | Page 46

In shuffling a pack of 52 playing cards, four are accidently dropped; find the chance that the missing cards should be one from each suit.

Exercise 33.3 | Q 12 | Page 46

From a deck of 52 cards, four cards are drawn simultaneously, find the chance that they will be the four honours of the same suit.

Exercise 33.3 | Q 13 | Page 46

Tickets numbered from 1 to 20 are mixed up together and then a ticket is drawn at random. What is the probability that the ticket has a number which is a multiple of 3 or 7?

Exercise 33.3 | Q 14 | Page 46

A bag contains 6 red, 4 white and 8 blue balls. if three balls are drawn at random, find the probability that one is red, one is white and one is blue.

Exercise 33.3 | Q 15.1 | Page 46

A bag contains 7 white, 5 black and 4 red balls. If two balls are drawn at random, find the probability that both the balls are white

Exercise 33.3 | Q 15.2 | Page 46

A bag contains 7 white, 5 black and 4 red balls. If two balls are drawn at random, find the probability that one ball is black and the other red

Exercise 33.3 | Q 15.3 | Page 46

A bag contains 7 white, 5 black and 4 red balls. If two balls are drawn at random, find the probability that both the balls are of the same colour.

Exercise 33.3 | Q 16.1 | Page 46

A bag contains 6 red, 4 white and 8 blue balls. If three balls are drawn at random, find the probability that one is red and two are white

Exercise 33.3 | Q 16.2 | Page 46

A bag contains 6 red, 4 white and 8 blue balls. If three balls are drawn at random, find the probability that two are blue and one is red

Exercise 33.3 | Q 16.3 | Page 46

A bag contains 6 red, 4 white and 8 blue balls. If three balls are drawn at random, find the probability that one is red

Exercise 33.3 | Q 17.1 | Page 46

Five cards are drawn from a pack of 52 cards. What is the chance that these 5 will contain at least one ace?

Exercise 33.3 | Q 17.2 | Page 46

Five cards are drawn from a pack of 52 cards. What is the chance that these 5 will contain at least one ace?

Exercise 33.3 | Q 18 | Page 46

The face cards are removed from a full pack. Out of the remaining 40 cards, 4 are drawn at random. what is the probability that they belong to different suits?

Exercise 33.3 | Q 19 | Page 46

In a hand at Whist, what is the probability that four kings are held by a specified player?

Exercise 33.3 | Q 20 | Page 46

There are four men and six women on the city councils. If one council member is selected for a committee at random, how likely is that it is a women?

Exercise 33.3 | Q 21 | Page 47

Find the probability that in a random arrangement of the letters of the word 'SOCIAL' vowels come together.

Exercise 33.3 | Q 22 | Page 47

The letters of the word' CLIFTON' are placed at random in a row. What is the chance that two vowels come together?

Exercise 33.3 | Q 23 | Page 47

The letters of the word 'FORTUNATES' are arranged at random in a row. What is the chance that the two 'T' come together.

Exercise 33.3 | Q 24 | Page 47

Find the probability that in a random arrangement of the letters of the word 'UNIVERSITY', the two I's do not come together.

Exercise 33.3 | Q 25.1 | Page 47

A committee of two persons is selected from two men and two women. What is the probability that the committee will have  no man?

Exercise 33.3 | Q 25.2 | Page 47

A committee of two persons is selected from two men and two women. What is the probability that the committee will have one man?

Exercise 33.3 | Q 25.3 | Page 47

A committee of two persons is selected from two men and two women. What is the probability that the committee will have  two men?

Exercise 33.3 | Q 26 | Page 47

If odds against an event be 7 : 9, find the probability of non-occurrence of this event.

Exercise 33.3 | Q 27 | Page 47

Two balls are drawn at random from a bag containing 2 white, 3 red, 5 green and 4 black balls, one by one without, replacement. Find the probability that both the balls are of different colours.

Exercise 33.3 | Q 28.1 | Page 47

Two unbiased dice are thrown. Find the probability that  neither a doublet nor a total of 8 will appear

Exercise 33.3 | Q 28.2 | Page 47

Two unbiased dice are thrown. Find the probability that the sum of the numbers obtained on the two dice is neither a multiple of 2 nor a multiple of 3

Exercise 33.3 | Q 29.1 | Page 47

A bag contains 8 red, 3 white and 9 blue balls. If three balls are drawn at random, determine the probability that all the three balls are blue balls

Exercise 33.3 | Q 29.2 | Page 47

A bag contains 8 red, 3 white and 9 blue balls. If three balls are drawn at random, determine the probability that  all the balls are of different colours.

Exercise 33.3 | Q 30 | Page 47

A bag contains 5 red, 6 white and 7 black balls. Two balls are drawn at random. What is the probability that both balls are red or both are black?

Exercise 33.3 | Q 31.1 | Page 47

If a letter is chosen at random from the English alphabet, find the probability that the letter is  a vowel .

Exercise 33.3 | Q 31.2 | Page 47

If a letter is chosen at random from the English alphabet, find the probability that the letter is a consonant .

Exercise 33.3 | Q 32 | Page 47

In a lottery, a person chooses six different numbers at random from 1 to 20, and if these six numbers match with six number already fixed by the lottery committee, he wins the prize. What is the probability of winning the prize in the game?

Exercise 33.3 | Q 33.1 | Page 47

20 cards are numbered from 1 to 20. One card is drawn at random. What is the probability that the number on the cards is a multiple of 4?

Exercise 33.3 | Q 33.2 | Page 47

20 cards are numbered from 1 to 20. One card is drawn at random. What is the probability that the number on the cards is not a multiple of 4?

Exercise 33.3 | Q 33.3 | Page 47

20 cards are numbered from 1 to 20. One card is drawn at random. What is the probability that the number on the cards is odd?

Exercise 33.3 | Q 33.4 | Page 47

20 cards are numbered from 1 to 20. One card is drawn at random. What is the probability that the number on the cards is greater than 12?

Exercise 33.3 | Q 33.5 | Page 47

20 cards are numbered from 1 to 20. One card is drawn at random. What is the probability that the number on the cards is  divisible by 5?

Exercise 33.3 | Q 33.6 | Page 47

20 cards are numbered from 1 to 20. One card is drawn at random. What is the probability that the number on the cards is not a multiple of 6?

Exercise 33.3 | Q 34.1 | Page 47

Two dice are thrown. Find the odds in favour of getting the sum 4.

Exercise 33.3 | Q 34.2 | Page 47

Two dice are thrown. Find the odds in favour of getting the sum 5.

Exercise 33.3 | Q 34.3 | Page 47

Two dice are thrown. Find the odds in favour of getting the sum  What are the odds against getting the sum 6?

Exercise 33.3 | Q 35 | Page 47

What are the odds in favour of getting a spade if the card drawn from a well-shuffled deck of cards? What are the odds in favour of getting a king?

Exercise 33.3 | Q 36.1 | Page 47

A box contains 10 red marbles, 20 blue marbles and 30 green marbles. 5 marbles are drawn at random. From the box, what is the probability that all are blue?

Exercise 33.3 | Q 36.2 | Page 47

A box contains 10 red marbles, 20 blue marbles and 30 green marbles. 5 marbles are drawn at random. From the box, what is the probability that  at least one is green?

Exercise 33.3 | Q 37.1 | Page 47

A box contains 6 red marbles numbered 1 through 6 and 4 white marbles numbered from 12 through 15. Find the probability that a marble drawn is white .

Exercise 33.3 | Q 37.2 | Page 47

A box contains 6 red marbles numbered 1 through 6 and 4 white marbles numbered from 12 through 15. Find the probability that a marble drawn is white and odd numbered .

Exercise 33.3 | Q 37.3 | Page 47

A box contains 6 red marbles numbered 1 through 6 and 4 white marbles numbered from 12 through 15. Find the probability that a marble drawn is even numbered

Exercise 33.3 | Q 37.4 | Page 47

A box contains 6 red marbles numbered 1 through 6 and 4 white marbles numbered from 12 through 15. Find the probability that a marble drawn is red or even numbered.

Exercise 33.3 | Q 38.1 | Page 47

A class consists of 10 boys and 8 girls. Three students are selected at random. What is the probability that the selected group has  all boys?

Exercise 33.3 | Q 38.2 | Page 47

A class consists of 10 boys and 8 girls. Three students are selected at random. What is the probability that the selected group has  all girls?

Exercise 33.3 | Q 38.3 | Page 47

A class consists of 10 boys and 8 girls. Three students are selected at random. What is the probability that the selected group has 1 boys and 2 girls?

Exercise 33.3 | Q 38.4 | Page 47

A class consists of 10 boys and 8 girls. Three students are selected at random. What is the probability that the selected group has  at least one girl?

Exercise 33.3 | Q 38.5 | Page 47

A class consists of 10 boys and 8 girls. Three students are selected at random. What is the probability that the selected group has  at most one girl?

Exercise 33.3 | Q 39 | Page 47

Five cards are drawn from a well-shuffled pack of 52 cards. Find the probability that all the five cards are hearts.

Exercise 33.3 | Q 40.1 | Page 48

A bag contains tickets numbered from 1 to 20. Two tickets are drawn. Find the probability that  both the tickets have prime numbers on them

Exercise 33.3 | Q 40.2 | Page 48

A bag contains tickets numbered from 1 to 20. Two tickets are drawn. Find the probability that  on one there is a prime number and on the other there is a multiple of 4.as

Exercise 33.3 | Q 41.1 | Page 48

An urn contains 7 white, 5 black and 3 red balls. Two balls are drawn at random. Find the probability that  both the balls are red .

Exercise 33.3 | Q 41.2 | Page 48

An urn contains 7 white, 5 black and 3 red balls. Two balls are drawn at random. Find the probability that one ball is red and the other is black

Exercise 33.3 | Q 41.3 | Page 48

An urn contains 7 white, 5 black and 3 red balls. Two balls are drawn at random. Find the probability that  one ball is white.

Exercise 33.3 | Q 42.1 | Page 48

Which of the cannot be valid assignment of probability for elementary events or outcomes of sample space S =  {w1w2w3w4w5w6w7}:

 Elementary events: w1 w2 w3 w4 w5 w6 w7 (i) 0.1 0.01 0.05 0.03 0.01 0.2 0.6
Exercise 33.3 | Q 42.2 | Page 48

Which of the cannot be valid assignment of probability for elementary events or outcomes of sample space S =  {w1w2w3w4w5w6w7}:

 Elementary events: w1 w2 w3 w4 w5 w6 w7 (ii) $\frac{1}{7}$ $\frac{1}{7}$ $\frac{1}{7}$ $\frac{1}{7}$ $\frac{1}{7}$ $\frac{1}{7}$ $\frac{1}{7}$
Exercise 33.3 | Q 42.3 | Page 48

Which of the cannot be valid assignment of probability for elementary events or outcomes of sample space S =  {w1w2w3w4w5w6w7}:

 Elementary events: w1 w2 w3 w4 w5 w6 w7 (iii) 0.7 0.06 0.05 0.04 0.03 0.2 0.1
Exercise 33.3 | Q 42.4 | Page 48

Which of the cannot be valid assignment of probability for elementary events or outcomes of sample space S =  {w1w2w3w4w5w6w7}:

 Elementary events: w1 w2 w3 w4 w5 w6 w7 (iv) $\frac{1}{14}$ $\frac{2}{14}$ $\frac{3}{14}$ $\frac{4}{14}$ $\frac{5}{14}$ $\frac{6}{14}$ $\frac{15}{14}$
Exercise 33.3 | Q 43 | Page 48

In a single throw of three dice, find the probability of getting the same number on all the three dice.

Exercise 33.3 | Q 44.1 | Page 48

A box contains 100 bulbs, 20 of which are defective. 10 bulbs are selected for inspection. Find the probability that: all 10 are defective

Exercise 33.3 | Q 44.2 | Page 48

A box contains 100 bulbs, 20 of which are defective. 10 bulbs are selected for inspection. Find the probability that all 10 are good

Exercise 33.3 | Q 44.3 | Page 48

A box contains 100 bulbs, 20 of which are defective. 10 bulbs are selected for inspection. Find the probability thatat least one is defective

Exercise 33.3 | Q 44.4 | Page 48

A box contains 100 bulbs, 20 of which are defective. 10 bulbs are selected for inspection. Find the probability that none is defective

Exercise 33.3 | Q 45 | Page 48

If odds in favour of an event be 2 : 3, find the probability of occurrence of this event.

Exercise 33.4[Pages 67 - 69]

### RD Sharma solutions for Class 11 Mathematics Textbook Chapter 33 ProbabilityExercise 33.4[Pages 67 - 69]

Exercise 33.4 | Q 1.1 | Page 67

If A and B be mutually exclusive events associated with a random experiment such that P(A) = 0.4 and P(B) = 0.5, then find

P (A ∪ B)

Exercise 33.4 | Q 1.1 | Page 67

If A and B be mutually exclusive events associated with a random experiment such that P(A) = 0.4 and P(B) = 0.5, then find

$P (\bar{ A } \cap \bar{ B} )$

Exercise 33.4 | Q 1.1 | Page 67

If A and B be mutually exclusive events associated with a random experiment such that P(A) = 0.4 and P(B) = 0.5, then find

P ( $\bar{ A}$ ∩ B)

Exercise 33.4 | Q 1.1 | Page 67

If A and B be mutually exclusive events associated with a random experiment such that P(A) = 0.4 and P(B) = 0.5, then find
P (A ∩$\bar{ B }$ ).

Exercise 33.4 | Q 1.2 | Page 67

A and B are two events such that P (A) = 0.54, P (B) = 0.69 and P (A ∩ B) = 0.35. Find
P (A ∪ B)

Exercise 33.4 | Q 1.2 | Page 67

A and B are two events such that P (A) = 0.54, P (B) = 0.69 and P (A ∩ B) = 0.35. Find

$P (\bar{ A } \cap \bar{ B } )$

Exercise 33.4 | Q 1.2 | Page 67

A and B are two events such that P (A) = 0.54, P (B) = 0.69 and P (A ∩ B) = 0.35. Find
P (A ∩  $\bar{ B }$ )

Exercise 33.4 | Q 1.2 | Page 67

A and B are two events such that P (A) = 0.54, P (B) = 0.69 and P (A ∩ B) = 0.35. Find

P (B ∩ $\bar{ A }$ )

Exercise 33.4 | Q 1.3 | Page 67

Fill in the blank in the table:

 P (A) P (B) P (A ∩ B) P(A∪ B) $\frac{1}{3}$ $\frac{1}{5}$ $\frac{1}{15}$ ......
Exercise 33.4 | Q 1.3 | Page 67

Fill in the blank in the table:

 P (A) P (B) P (A ∩ B) P(A∪ B) 0.35 .... 0.25 0.6
Exercise 33.4 | Q 1.3 | Page 67

Fill in the blank in the table:

 P (A) P (B) P (A ∩ B) P(A∪ B) 0.5 0.35 ..... 0.7
Exercise 33.4 | Q 2 | Page 68

If and B are two events associated with a random experiment such that P(A) = 0.3, P (B) = 0.4 and P (A ∪ B) = 0.5, find P (A ∩ B).

Exercise 33.4 | Q 3 | Page 68

If A and B are two events associated with a random experiment such that
P(A) = 0.5, P(B) = 0.3 and P (A ∩ B) = 0.2, find P (A ∪ B).

Exercise 33.4 | Q 4 | Page 68

If A and B are two events associated with a random experiment such that
P (A ∪ B) = 0.8, P (A ∩ B) = 0.3 and P $(\bar{A} )$= 0.5, find P(B).

Exercise 33.4 | Q 5 | Page 68

Given two mutually exclusive events A and B such that P(A) = 1/2 and P(B) = 1/3, find P(A or B).

Exercise 33.4 | Q 6 | Page 68

There are three events ABC one of which must and only one can happen, the odds are 8 to 3 against A, 5 to 2 against B, find the odds against C

Exercise 33.4 | Q 7 | Page 68

One of the two events must happen. Given that the chance of one is two-third of the other, find the odds in favour of the other.

Exercise 33.4 | Q 8 | Page 68

A card is drawn at random from a well-shuffled deck of 52 cards. Find the probability of its being a spade or a king.

Exercise 33.4 | Q 9 | Page 68

In a single throw of two dice, find the probability that neither a doublet nor a total of 9 will appear.

Exercise 33.4 | Q 10 | Page 68

A natural number is chosen at random from amongst first 500. What is the probability that the number so chosen is divisible by 3 or 5?

Exercise 33.4 | Q 11 | Page 68

A dice is thrown twice. What is the probability that at least one of the two throws come up with the number 3?

Exercise 33.4 | Q 12 | Page 68

A card is drawn from a deck of 52 cards. Find the probability of getting an ace or a spade card.

Exercise 33.4 | Q 13 | Page 68

The probability that a student will pass the final examination in both English and Hindi is 0.5 and the probability of passing neither is 0.1. If the probability of passing the English Examination is 0.75. What is the probability of passing the Hindi Examination?

Exercise 33.4 | Q 14 | Page 68

One number is chosen from numbers 1 to 100. Find the probability that it is divisible by 4 or 6?

Exercise 33.4 | Q 15 | Page 68

From a well shuffled deck of 52 cards, 4 cards are drawn at random. What is the probability that all the drawn cards are of the same colour.

Exercise 33.4 | Q 16 | Page 68

100 students appeared for two examination, 60 passed the first, 50 passed the second and 30 passed both. Find the probability that a student selected at random has passed at least one examination.

Exercise 33.4 | Q 17 | Page 68

A box contains 10 white, 6 red and 10 black balls. A ball is drawn at random from the box. What is the probability that the ball drawn is either white or red?

Exercise 33.4 | Q 18 | Page 68

In a race, the odds in favour of horses ABCD are 1 : 3, 1 : 4, 1 : 5 and 1 : 6 respectively. Find probability that one of them wins the race.

Exercise 33.4 | Q 19 | Page 68

The probability that a person will travel by plane is 3/5 and that he will travel by trains is 1/4. What is the probability that he (she) will travel by plane or train?

Exercise 33.4 | Q 20 | Page 68

Two cards are drawn from a well shuffled pack of 52 cards. Find the probability that either both are black or both are kings.

Exercise 33.4 | Q 21 | Page 69

In an entrance test that is graded on the basis of two examinations, the probability of a randomly chosen student passing the first examination is 0.8 and the probability of passing the second examination is 0.7. The probability of passing at least one of them is 0.95. What is the probability of passing both?

Exercise 33.4 | Q 22 | Page 69

A box contains 30 bolts and 40 nuts. Half of the bolts and half of the nuts are rusted. If two items are drawn at random, what is the probability that either both are rusted or both are bolts?

Exercise 33.4 | Q 23 | Page 69

An integer is chosen at random from first 200 positive integers. Find the probability that the integer is divisible by 6 or 8.

Exercise 33.4 | Q 24 | Page 69

Find the probability of getting 2 or 3 tails when a coin is tossed four times.

Exercise 33.4 | Q 25 | Page 69

Suppose an integer from 1 through 1000 is chosen at random, find the probability that the integer is a multiple of 2 or a multiple of 9.

Exercise 33.4 | Q 26 | Page 69

In a large metropolitan area, the probabilities are 0.87, 0.36, 0.30 that a family (randomly chosen for a sample survey) owns a colour television set, a black and white television set, or both kinds of sets. What is the probability that a family owns either any one or both kinds of sets?

Exercise 33.4 | Q 27.1 | Page 69

If A and B are mutually exclusive events such that P(A) = 0.35 and P(B) = 0.45, find P(A ∪ B)

Exercise 33.4 | Q 27.2 | Page 69

If A and B are mutually exclusive events such that P(A) = 0.35 and P(B) = 0.45, find P(A ∩ B)

Exercise 33.4 | Q 27.3 | Page 69

If A and B are mutually exclusive events such that P(A) = 0.35 and P(B) = 0.45, find P(A ∩ $\bar{ B }$ )

Exercise 33.4 | Q 27.4 | Page 69

If A and B are mutually exclusive events such that P(A) = 0.35 and P(B) = 0.45, find P($\bar{ A }$ ∩  $\bar{B}$ )

Exercise 33.4 | Q 28.1 | Page 69

A sample space consists of 9 elementary events E1E2E3, ..., E9 whose probabilities are
P(E1) = P(E2) = 0.08, P(E3) = P(E4) = P(E5) = 0.1, P(E6) = P(E7) = 0.2, P(E8) = P(E9) = 0.07
Suppose A = {E1E5E8}, B = {E2E5E8, E9}

Compute P(A)P(B) and P(A ∩ B).

Exercise 33.4 | Q 28.2 | Page 69

A sample space consists of 9 elementary events E1E2E3, ..., E9 whose probabilities are
P(E1) = P(E2) = 0.08, P(E3) = P(E4) = P(E5) = 0.1, P(E6) = P(E7) = 0.2, P(E8) = P(E9) = 0.07
Suppose A = {E1E5E8}, B = {E2E5E8, E9}

Using the addition law of probability, find P(A ∪ B).

Exercise 33.4 | Q 28.3 | Page 69

A sample space consists of 9 elementary events E1E2E3, ..., E9 whose probabilities are
P(E1) = P(E2) = 0.08, P(E3) = P(E4) = P(E5) = 0.1, P(E6) = P(E7) = 0.2, P(E8) = P(E9) = 0.07
Suppose A = {E1E5E8}, B = {E2E5E8, E9}

List the composition of the event A ∪ B, and calculate P(A ∪ B) by addting the probabilities of elementary events.

Exercise 33.4 | Q 28.4 | Page 69

A sample space consists of 9 elementary events E1E2E3, ..., E9 whose probabilities are
P(E1) = P(E2) = 0.08, P(E3) = P(E4) = P(E5) = 0.1, P(E6) = P(E7) = 0.2, P(E8) = P(E9) = 0.07
Suppose A = {E1E5E8}, B = {E2E5E8, E9}

Calculate $P\left( \bar{ B} \right)$  from P(B), also calculate $P\left( \bar{ B } \right)$  directly from the elementary events of $\bar{ B }$ .

[Page 71]

### RD Sharma solutions for Class 11 Mathematics Textbook Chapter 33 Probability[Page 71]

Q 2 | Page 71

n (≥ 3) persons are sitting in a row. Two of them are selected. Write the probability that they are together.

Q 3 | Page 71

A single letter is selected at random from the word 'PROBABILITY'. What is the probability that it is a vowel?

Q 4 | Page 71

What is the probability that a leap year will have 53 Fridays or 53 Saturdays?

Q 5 | Page 71

Three dice are thrown simultaneously. What is the probability of getting 15 as the sum?

Q 6 | Page 71

If the letters of the word 'MISSISSIPPI' are written down at random in a row, what is the probability that four S's come together.

Q 7 | Page 71

What is the probability that the 13th days of a randomly chosen month is Friday?

Q 8 | Page 71

Three of the six vertices of a regular hexagon are chosen at random. What is the probability that the triangle with these vertices is equilateral.

Q 9 | Page 71

If E and E2 are independent evens, write the value of P $\left( ( E_1 \cup E_2 ) \cap (E \cap E_2 ) \right)$

Q 10 | Page 71

If A and B are two independent events such that $P (A \cap B) = \frac{1}{6}\text{ and } P (A \cap B) = \frac{1}{3},$  then write the values of P (A) and P (B).

[Pages 71 - 73]

### RD Sharma solutions for Class 11 Mathematics Textbook Chapter 33 Probability[Pages 71 - 73]

Q 1 | Page 71

One card is drawn from a pack of 52 cards. The probability that it is the card of a king or spade is

•  1/26

• 3/26

•  4/13

•  3/13

Q 2 | Page 71

Two dice are thrown together. The probability that at least one will show its digit greater than 3 is

• 1/4

•  3/4

•  1/2

• 1/8

Q 3 | Page 71

Two dice are thrown simultaneously. The probability of obtaining a total score of 5 is

•  1/18

•  1/12

•  1/9

• none of these

Q 4 | Page 71

Two dice are thrown simultaneously. The probability of obtaining total score of seven is

• 5/36

•  6/36

• 7/36

• 8/36

Q 5 | Page 71

The probability of getting a total of 10 in a single throw of two dices is

•  1/9

• 1/12

•  1/6

•  5/36

Q 6 | Page 71

A card is drawn at random from a pack of 100 cards numbered 1 to 100. The probability of drawing a number which is a square is

• 1/5

•  2/5

• 1/10

• none of these

Q 7 | Page 71

A bag contains 3 red, 4 white and 5 blue balls. All balls are different. Two balls are drawn at random. The probability that they are of different colour is

•  47/66

•  10/33

•  1/3

• 1

Q 8 | Page 71

Two dice are thrown together. The probability that neither they show equal digits nor the sum of their digits is 9 will be

•  13/15

•  13/18

•  1/9

•  8/9

Q 9 | Page 71

Four persons are selected at random out of 3 men, 2 women and 4 children. The probability that there are exactly 2 children in the selection is

•  11/21

• 9/21

•  10/21

•  none of these

Q 10 | Page 71

The probabilities of happening of two events A and B are 0.25 and 0.50 respectively. If the probability of happening of A and B together is 0.14, then probability that neither Anor B happens is

•  0.39

•  0.25

•  0.11

•  none of these

Q 11 | Page 72

A die is rolled, then the probability that a number 1 or 6 may appear is

• 2/3

•  5/6

• 1/3

•  1/2

Q 12 | Page 72

Six boys and six girls sit in a row randomly. The probability that all girls sit together is

•  1/122

• 1/112

•  1/102

•  1/132

Q 13 | Page 72

The probabilities of three mutually exclusive events AB and are given by 2/3, 1/4 and 1/6 respectively. The statement

•  is true

•  is false

• nothing can be said

•  could be either

Q 14 | Page 72

If $\frac{(1 - 3p)}{2}, \frac{(1 + 4p)}{3}, \frac{(1 + p)}{6}$ are the probabilities of three mutually exclusive and exhaustive events, then the set of all values of p is

• (0, 1)

•  (−1/4, 1/3)

• (0, 1/3)

• (0, ∞)

Q 15 | Page 72

A pack of cards contains 4 aces, 4 kings, 4 queens and 4 jacks. Two cards are drawn at random. The probability that at least one of them is an ace is

•  1/5

•  3/16

•  9/20

• 1/9

Q 16 | Page 72

If three dice are throw simultaneously, then the probability of getting a score of 5 is

• 5/216

• 1/6

•  1/36

•  none of these

Q 17 | Page 72

One of the two events must occur. If the chance of one is 2/3 of the other, then odds in favour of the other are

•  1 : 3

• 3 : 1

•  2 : 3

•  3 : 2

Q 18 | Page 72

The probability that a leap year will have 53 Fridays or 53 Saturdays is

•  2/7

•  3/7

• 4/7

• 1/7

Q 19 | Page 72

A person write 4 letters and addresses 4 envelopes. If the letters are placed in the envelopes at random, then the probability that all letters are not placed in the right envelopes, is

• 1/4

• 11/24

•  15/24

• 23/24

Q 20 | Page 72

A and B are two events such that P (A) = 0.25 and P (B) = 0.50. The probability of both happening together is 0.14. The probability of both A and B not happening is

•  0.39

•  0.25

•  0.11

•  none of these

Q 21 | Page 72

If the probability of A to fail in an examination is $\frac{1}{5}$  and that of B is $\frac{3}{10}$ . Then, the probability that either A or B fails is

• 1/2

• 11/25

•  19/50

•  none of these

Q 22 | Page 72

A box contains  10 good articles and 6 defective articles. One item is drawn at random. The probability that it is either good or has a defect, is

•  64/64

• 49/64

• 40/64

• 24/64

Q 23 | Page 72

Three integers are chosen at random from the first 20 integers. The probability that their product is even is

•  2/19

• 3/29

• 17/19

• 4/19

Q 24 | Page 72

Out of 30 consecutive integers, 2 are chosen at random. The probability that their sum is odd, is

•  14/29

•  16/29

•  15/29

•  10/29

Q 25 | Page 72

A bag contains 5 black balls, 4 white balls and 3 red balls. If a ball is selected randomwise, the probability that it is black or red ball is

•  1/3

• 1/4

•  5/12

•  2/3

Q 26 | Page 72

Two dice are thrown simultaneously. The probability of getting a pair of aces is

• 1/36

•  1/3

• 1/6

• none of these

Q 27 | Page 72

An urn contains 9 balls two of which are red, three blue and four black. Three balls are drawn at random. The probability that they are of the same colour is

•  5/84

•  3/9

•  3/7

• 7/17

Q 28 | Page 72

Five persons entered the lift cabin on the ground floor of an 8 floor house. Suppose that each of them independently and with equal probability can leave the cabin at any floor beginning with the first, then the probability of all 5 persons leaving at different floor is

•  $\frac{^{7}{}{P}_5}{7^5}$

• $\frac{7^5}{^{7}{}{P}_5}$

•  $\frac{6}{^{6}{}{P}_5}$

•  $\frac{^{5}{}{P}_5}{5^5}$

Q 29 | Page 73

A box contains 10 good articles and 6 with defects. One item is drawn at random. The probability that it is either good or has a defect is

•  64/64

•  49/64

•  40/64

• 24/64

Q 30 | Page 73

A box contains 6 nails and 10 nuts. Half of the nails and half of the nuts are rusted. If one item is chosen at random, the probability that it is rusted or is a nail is

•  3/16

•  5/16

•  11/16

•  14/16

Q 31 | Page 73

If S is the sample space and P(A) = $\frac{1}{3}$  P(B) and S = A ∪ B, where A and B are two mutually exclusive events, then P (A) =

•  1/4

• 1/2

• 3/4

•  3/8

Q 32 | Page 73

One mapping is selected at random from all mappings of the set A = {1, 2, 3, ..., n} into itself. The probability that the mapping selected is one to one is

• $\frac{1}{n^n}$

• $\frac{1}{n!}$

•   $\frac{\left( n - 1 \right)!}{n^{n - 1}}$

•   None of these

Q 33 | Page 73

If ABC are three mutually exclusive and exhaustive events of an experiment such that 3 P(A) = 2 P(B) = P(C), then P(A) is equal to

•  $\frac{1}{11}$

•  $\frac{2}{11}$

•   $\frac{5}{11}$

•  $\frac{6}{11}$

Q 34 | Page 73

If A and B are mutually exclusive events then

•  $P\left( A \right) \leq P\left( B \right)$

• $P\left( A \right) \geq P\left( B \right)$

•  $P\left( A \right) < P\left( B \right)$

•  None of these

Q 35 | Page 73

If P(A ∪ B) = P(A ∩ B) for any two events A and B, then

• P(A) = P(B)

•  P(A) > P(B)

•  P(A) < P(B

•  None of these

Q 36 | Page 73

Three numbers are chosen from 1 to 20. The probability that they are not consecutive is

• $\frac{186}{190}$

• $\frac{187}{190}$

• $\frac{188}{190}$

• $\frac{18}{^{20}{}{C}_3}$

Q 37 | Page 73

6 boys and 6 girls sit in a row at random. The probability that all the girls sit together is

• $\frac{1}{432}$

• $\frac{12}{431}$

• $\frac{1}{132}$

•  None of these

Q 38 | Page 73

Without repetition of the numbers, four digit numbers are formed with the numbers 0, 2, 3, 5. The probability of such a number divisible by 5 is

•  $\frac{1}{5}$

•  $\frac{4}{5}$

• $\frac{1}{30}$

•  $\frac{5}{9}$

Q 39 | Page 73

If the probability for A to fail in an examination is 0.2 and that for B is 0.3, then the probability that either A or B fails is

•  > 0.5

• 0.5

•  ≤ 0.5

• 0

Q 40 | Page 73

Three digit numbers are formed using the digits 0, 2, 4, 6, 8. A number is chosen at random out of these numbers. What is the probability that this number has the same digits?

• $\frac{1}{16}$

• $\frac{16}{25}$

• $\frac{1}{645}$

• $\frac{1}{25}$

## Chapter 33: Probability

Exercise 33.1Exercise 33.2Exercise 33.3Exercise 33.4Others ## RD Sharma solutions for Class 11 Mathematics Textbook chapter 33 - Probability

RD Sharma solutions for Class 11 Mathematics Textbook chapter 33 (Probability) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CBSE Class 11 Mathematics Textbook solutions in a manner that help students grasp basic concepts better and faster.

Further, we at Shaalaa.com provide such solutions so that students can prepare for written exams. RD Sharma textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.

Concepts covered in Class 11 Mathematics Textbook chapter 33 Probability are Exhaustive Events, Mutually Exclusive Events, Axiomatic Approach to Probability, Probability of 'Not', 'And' and 'Or' Events, Random Experiments, Introduction of Event, Occurrence of an Event, Types of Events, Algebra of Events.

Using RD Sharma Class 11 solutions Probability exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in RD Sharma Solutions are important questions that can be asked in the final exam. Maximum students of CBSE Class 11 prefer RD Sharma Textbook Solutions to score more in exam.

Get the free view of chapter 33 Probability Class 11 extra questions for Class 11 Mathematics Textbook and can use Shaalaa.com to keep it handy for your exam preparation

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