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

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

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

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

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.

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

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.

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

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.

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.

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

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.

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?

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

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.

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

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?

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?

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.

In a single throw of a die describe the event:

A = Getting a number less than 7

In a single throw of a die describe the event:

B = Getting a number greater than 7

In a single throw of a die describe the event:

 C = Getting a multiple of 3

In a single throw of a die describe the event:

D = Getting a number less than 4

In a single throw of a die describe the event:

E = Getting an even number greater than 4

In a single throw of a die describe the event:

F = Getting a number not less than 3.
Also, find A ∪ B, A ∩ B, B ∩ C, E ∩ F, D ∩ F and \[ \bar { F } \] . 

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

Three coins are tossed. Describe. three events A, B and C which are mutually exclusive and exhaustive.

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

Three coins are tossed. Describe.

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 ∪ B, A ∩ B, A ∪ C, A ∩ C
Which pairs of events are mutually exclusive?

Two dice are thrown. The events A, B, C, D, E 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 B, B or C, B and C, A and E, A or F, A and F

Two dice are thrown. The events A, B, C, D, E 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:

1. A and B are mutually exclusive.
2. A and B are mutually exclusive and exhaustive events.
3. A and C are mutually exclusive events.
4. C and D are mutually exclusive and exhaustive events.
5. C, D and E are mutually exclusive and exhaustive events.
6. A' and B' are mutually exclusive events.
7. A, B, F are mutually exclusive and exhaustive events. 

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?

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

What is the sample space of the experiment?

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

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

A dice is thrown. Find the probability of getting:

 2 or 4

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

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

8 as the sum

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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.

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.

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?

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

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

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.

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

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

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

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

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

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?

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

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

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

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

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

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

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.

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

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

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 

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.

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?

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

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

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?

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?

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?

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?

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?

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?

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?

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

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

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

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?

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?

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 .

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 .

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

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.

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?

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?

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?

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?

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?

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

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

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

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 .

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

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. 

Which of the cannot be valid assignment of probability for elementary events or outcomes of sample space S =  {w₁, w₂, w₃, w₄, w₅, w₆, w₇}:

Which of the cannot be valid assignment of probability for elementary events or outcomes of sample space S =  {w₁, w₂, w₃, w₄, w₅, w₆, w₇}:

Which of the cannot be valid assignment of probability for elementary events or outcomes of sample space S =  {w₁, w₂, w₃, w₄, w₅, w₆, w₇}:

Which of the cannot be valid assignment of probability for elementary events or outcomes of sample space S =  {w₁, w₂, w₃, w₄, w₅, w₆, w₇}:

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

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

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

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

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

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)

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

\[P (\bar{ A } \cap \bar{ B} )\]

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 ∩\[\bar{ B } \] ).

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)

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).

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 ∩ \[\bar{ A } \] )

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 ∩  \[\bar{ B } \] )

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

\[P (\bar{ A } \cap \bar{ B } )\]

Fill in the blank in the table:

Fill in the blank in the table:

Fill in the blank in the table:

If A 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).

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).

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).

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

There are three events A, B, C 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

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.

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.

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

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?

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

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

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?

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

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.

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.

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?

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

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?

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

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?

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?

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

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.

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?  

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

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

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

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

A sample space consists of 9 elementary events E₁, E₂, E₃, ..., 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 = {E₁, E₅, E₈}, B = {E₂, E₅, E₈, E₉}   

 Compute P(A), P(B) and P(A ∩ B).

A sample space consists of 9 elementary events E₁, E₂, E₃, ..., 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 = {E₁, E₅, E₈}, B = {E₂, E₅, E₈, E₉}   

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

A sample space consists of 9 elementary events E₁, E₂, E₃, ..., 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 = {E₁, E₅, E₈}, B = {E₂, E₅, E₈, E₉}   

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

A sample space consists of 9 elementary events E₁, E₂, E₃, ..., 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 = {E₁, E₅, E₈}, B = {E₂, E₅, E₈, E₉}   

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

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

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.

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

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).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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) =

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

If A, B, C 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 

If A and B are mutually exclusive events then 

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

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

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

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

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

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?