#### Chapters

Chapter 2 - Banking (Recurring Deposit Account)

Chapter 3 - Shares and Dividend

Chapter 4 - Linear Inequations (In one variable)

Chapter 5 - Quadratic Equations

Chapter 6 - Solving (simple) Problems (Based on Quadratic Equations)

Chapter 7 - Ratio and Proportion (Including Properties and Uses)

Chapter 8 - Remainder and Factor Theorems

Chapter 9 - Matrices

Chapter 10 - Arithmetic Progression

Chapter 11 - Geometric Progression

Chapter 12 - Reflection

Chapter 13 - Section and Mid-Point Formula

Chapter 14 - Equation of a Line

Chapter 15 - Similarity (With Applications to Maps and Models)

Chapter 16 - Loci (Locus and Its Constructions)

Chapter 17 - Circles

Chapter 18 - Tangents and Intersecting Chords

Chapter 19 - Constructions (Circles)

Chapter 20 - Cylinder, Cone and Sphere

Chapter 21 - Trigonometrical Identities

Chapter 22 - Height and Distances

Chapter 23 - Graphical Representation

Chapter 24 - Measure of Central Tendency(Mean, Median, Quartiles and Mode)

Chapter 25 - Probability

## Chapter 25 - Probability

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A coin is tossed once. Find the probability of:

getting a tail

Nine cards (identical in all respects) are numbered 2 to 10. A card is selected from them at random. Find the probability that the card selected will be:

an even number

A coin is tossed once. Find the probability of:

not getting a tail

Nine cards (identical in all respects) are numbered 2 to 10. A card is selected from them at random. Find the probability that the card selected will be:

a multiple of 3

Nine cards (identical in all respects) are numbered 2 to 10. A card is selected from them at random. Find the probability that the card selected will be:

an even number and a multiple of 3

an even number or a multiple of 3

Hundred identical cards are numbered from 1 to 100. The cards The cards are well shuffled and then a card is drawn. Find the probability that the number on card drawn is:

a multiple of 5

A bag contains 3 white, 5 black and 2 red balls, all of the same shape and size. A ball is drawn from the bag without looking into it, find the probability that the ball drawn

a black ball.

A bag contains 3 white, 5 black and 2 red balls, all of the same shape and size. A ball is drawn from the bag without looking into it, find the probability that the ball drawn

a red ball.

A bag contains 3 white, 5 black and 2 red balls, all of the same shape and size. A ball is drawn from the bag without looking into it, find the probability that the ball drawn

not a black ball.

In a single throw of a die, find the probability of getting a number:

greater than 4

In a single throw of a die, find the probability of getting a number:

less than or equal to 4

In a single throw of a die, find the probability of getting a number:

not greater than 4.

In a single throw of a die, find the probability of getting a number:

not greater than 4.

In a single throw of a die, find the probability that the number:

will be an even number.

In a single throw of a die, find the probability that the number: will not be an even number.

In a single throw of a die, find the probability that the number:

will not be an even number.

From a well shuffled deck of 52 cards, one card is drawn. Find the probability that the card drawn will:

be a black card.

From a well shuffled deck of 52 cards, one card is drawn. Find the probability that the card drawn will:

not be a red card.

From a well shuffled deck of 52 cards, one card is drawn. Find the probability that the card drawn will:

be a red card.

be a face card.

From a well shuffled deck of 52 cards, one card is drawn. Find the probability that the card drawn will

be a face card of red colour.

If A and B are two complementary events then what is the relation between P(A) and P(B)?

If the probability of happening an event A is 0.46. What will be the probability of not happening of the event A?

In a T.T. match between Geeta and Ritu, the probability of the winning of Ritu is 0.73. Find the probability of:

winning of Geeta

In a T.T. match between Geeta and Ritu, the probability of the winning of Ritu is 0.73. Find the probability of:

not winning of Ritu

In a race between Mahesh and John, the probability that John will lose the race is 0.54. Find the probability of:

(i) winning of Mahesh

(ii) winning of John

Write the probability of a sure event

Write the probability of an event when impossible

For an event E, write a relation representing the range of values of P(E)

In a single throw of die, find the probability of getting:

5

In a single throw of die, find the probability of getting:

8

In a single throw of die, find the probability of getting:

a number less than 8

In a single throw of die, find the probability of getting:

a prime number

A die is thrown once. Find the probability of getting:

an even number

A die is thrown once. Find the probability of getting:

a number between 3 and 8

A die is thrown once. Find the probability of getting:

an even number or a multiple of 3

following are cannot be the probability of an event ?

3/5

following are cannot be the probability of an event?

2.7

Which of the following cannot be the probability of an event?

43%

following are cannot be the probability of an event?

-0.6

following are cannot be the probability of an event?

-3.2

Which of the following cannot be the probability of an event?

0.35

A bag contains six identical black balls. A child withdraws one ball from the bag without looking into it. What is the probability that he takes out:

a white ball

A bag contains six identical black balls. A child withdraws one ball from the bag without looking into it. What is the probability that he takes out:

a black ball

A single letter is selected at random from the word ‘Probability’. Find the probability that it is a vowel.

Ramesh chooses a date at random in january for a party.

January |
|||||

Mon |
6 | 13 | 20 | 27 | |

Tue |
7 | 14 | 21 | 28 | |

Wed |
1 | 8 | 15 | 22 | 29 |

Thurs |
2 | 9 | 16 | 23 | 30 |

Fri |
3 | 10 | 17 | 24 | 31 |

sat |
4 | 11 | 18 | 25 | |

Sun |
5 | 12 | 19 | 26 |

Find the probability that the choose:

(1) a Wednesday

(2) a friday

(3) a tuesday or a saturday.

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Hundred identical cards are numbered from 1 to 100. The cards The cards are well shuffled and then a card is drawn. Find the probability that the number on card drawn is:

a multiple of 6

Hundred identical cards are numbered from 1 to 100. The cards The cards are well shuffled and then a card is drawn. Find the probability that the number on card drawn is:

between 40 and 60

not a red ball.

greater than 85

less than 48

From 25 identical cards, numbered 1, 2, 3, 4, 5, ……, 24, 25: one card is drawn at random. Find the probability that the number on the card drawn is a multiple of:

3

From 25 identical cards, numbered 1, 2, 3, 4, 5, ……, 24, 25: one card is drawn at random. Find the probability that the number on the card drawn is a multiple of:

5

From 25 identical cards, numbered 1, 2, 3, 4, 5, ……, 24, 25: one card is drawn at random. Find the probability that the number on the card drawn is a multiple of:

3 and 5

3 or 5

A die is thrown once. Find the probability of getting a number:

less than 3

A die is thrown once. Find the probability of getting a number:

greater than or equal to 4

A die is thrown once. Find the probability of getting a number:

less than 8

A die is thrown once. Find the probability of getting a number:

greater than 6

A book contains 85 pages. A page is chosen at random. What is the probability that the sum of the digits on the page is 8?

A pair of dice is thrown. Find the probability of getting a sum of 10 or more, if 5 appears on the first die.

If two coins are tossed once, what is the probability of getting:

both heads

If two coins are tossed once, what is the probability of getting:

at least one head.

If two coins are tossed once, what is the probability of getting:

both heads or both tails

Two dice are rolled together. Find the probability of getting:

a total of at least 10

Two dice are rolled together. Find the probability of getting:

a multiple of 2 on one die and an odd number on the other die.

A card is drawn from a well shuffled pack of 52 cards. Find the probability that the card drawn is:

a spade

A card is drawn from a well shuffled pack of 52 cards. Find the probability that the card drawn is:

a red card

A card is drawn from a well shuffled pack of 52 cards. Find the probability that the card drawn is:

a face card

A card is drawn from a well shuffled pack of 52 cards. Find the probability that the card drawn is:

5 of heart or diamond

A card is drawn from a well shuffled pack of 52 cards. Find the probability that the card drawn is:

Jack or queen

A card is drawn from a well shuffled pack of 52 cards. Find the probability that the card drawn is:

ace and king

A card is drawn from a well shuffled pack of 52 cards. Find the probability that the card drawn is:

a red and a king

A card is drawn from a well shuffled pack of 52 cards. Find the probability that the card drawn is:

a red or a king

A bag contains 16 colored balls. Six are green, 7 are red and 3 are white. A ball is chosen, without looking into the bag. Find the probability that the ball chosen is:

red

A bag contains 16 colored balls. Six are green, 7 are red and 3 are white. A ball is chosen, without looking into the bag. Find the probability that the ball chosen is:

not red

A bag contains 16 colored balls. Six are green, 7 are red and 3 are white. A ball is chosen, without looking into the bag. Find the probability that the ball chosen is:

white

not white

green or red

white or green

green or red or white

A ball is drawn at random from a box containing 12 white, 16 red and 20 green balls. Determine the probability that the ball drawn is:

white

A ball is drawn at random from a box containing 12 white, 16 red and 20 green balls. Determine the probability that the ball drawn is:

red

A ball is drawn at random from a box containing 12 white, 16 red and 20 green balls. Determine the probability that the ball drawn is:

red

not green

red or white

A card is drawn from a pack of 52 cards. Find the probability that the card drawn is:

an ace

A card is drawn from a pack of 52 cards. Find the probability that the card drawn is:

a black ace

A card is drawn from a pack of 52 cards. Find the probability that the card drawn is:

ace of diamonds

A card is drawn from a pack of 52 cards. Find the probability that the card drawn is:

not a club

A card is drawn from a pack of 52 cards. Find the probability that the card drawn is:

a queen or a jack

A card is drawn from a pack of 52 cards. Find the probability that the card drawn is:

a red card

A card is drawn from a pack of 52 cards. Find the probability that the card drawn is:

a black card

A card is drawn from a pack of 52 cards. Find the probability that the card drawn is:

a spade

Thirty identical cards are marked with numbers 1 to 30. If one card is drawn at random, find the probability that it is:

a multiple of 4 or 6

Thirty identical cards are marked with numbers 1 to 30. If one card is drawn at random, find the probability that it is:

a multiple of 3 and 5

Thirty identical cards are marked with numbers 1 to 30. If one card is drawn at random, find the probability that it is:

a multiple of 3 or 5

In a single throw of two dice, find the probability of:

a doublet

In a single throw of two dice, find the probability of:

a number less than 3 on each dice

In a single throw of two dice, find the probability of:

an odd number as a sum

In a single throw of two dice, find the probability of:

a total of at most 10

In a single throw of two dice, find the probability of:

an odd number on one dice and a number less than or equal to 4 on the other dice.

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A bag contains 3 red balls, 4 blue balls and 1 yellow ball, all the balls being identical in shape and size. If a ball is taken out of the bag without looking into it; find the probability that the ball is:

yellow

A bag contains 3 red balls, 4 blue balls and 1 yellow ball, all the balls being identical in shape and size. If a ball is taken out of the bag without looking into it; find the probability that the ball is:

red

A bag contains 3 red balls, 4 blue balls and 1 yellow ball, all the balls being identical in shape and size. If a ball is taken out of the bag without looking into it; find the probability that the ball is:

not yellow

neither yellow nor red

A dice is thrown once. What is the probability of getting a number:

greater than 2?

A dice is thrown once. What is the probability of getting a number:

less than or equal to 2?

From a well shuffled deck of 52 cards, one card is drawn. Find the probability that the card drawn is:

a face card

From a well shuffled deck of 52 cards, one card is drawn. Find the probability that the card drawn is:

not a face card

From a well shuffled deck of 52 cards, one card is drawn. Find the probability that the card drawn is:

a card with number 5 or 6

From a well shuffled deck of 52 cards, one card is drawn. Find the probability that the card drawn is

a card with number less than 8

a card with number between 2 and 9

In a match between A and B:

the probability of winning of A is 0.83. What is the probability of winning of B?

In a match between A and B:

the probability of losing the match is 0.49 for B. What is the probability of winning of A?

A and B are friends. Ignoring the leap year, find the probability that both friends will have:

different birthdays?

A and B are friends. Ignoring the leap year, find the probability that both friends will have:

the same birthday?

A man tosses two different coins (one of Rs 2 and another of Rs 5) simultaneously. What is the probability that he gets:

at least one head?

A man tosses two different coins (one of Rs 2 and another of Rs 5) simultaneously. What is the probability that he gets:** **

at most one head?

A box contains 7 red balls, 8 green balls and 5 white balls. A ball is drawn at random from the box. Find the probability that the ball is:

white

A box contains 7 red balls, 8 green balls and 5 white balls. A ball is drawn at random from the box. Find the probability that the ball is:

neither red nor white.

All the three face cards of spades are removed from a well shuffled pack of 52 cards. A card is then drawn at random from the remaining pack. Find the probability of getting:

a black face card

All the three face cards of spades are removed from a well shuffled pack of 52 cards. A card is then drawn at random from the remaining pack. Find the probability of getting:

a queen

All the three face cards of spades are removed from a well shuffled pack of 52 cards. A card is then drawn at random from the remaining pack. Find the probability of getting:

a black card

In a musical chairs game, a person has been advised to stop playing the music at any time within 40 seconds after its start. What is the probability that the music will stop within the first 15 seconds?

In a bundle of 50 shirts, 44 are good, 4 have minor defects and 2 have major defects. What is the probability that:

it is acceptable to a trader who accepts only a good shirt?

In a bundle of 50 shirts, 44 are good, 4 have minor defects and 2 have major defects. What is the probability that:

it is acceptable to a trader who rejects only a shirt with major defects?

Two dice are thrown at the same time. Find the probability that the sum of the two numbers appearing on the top of the dice is:

8

A bag contains a certain number of red balls. A ball is drawn. Find the probability that the ball drawn is:

red

Two dice are thrown at the same time. Find the probability that the sum of the two numbers appearing on the top of the dice is:

13

Two dice are thrown at the same time. Find the probability that the sum of the two numbers appearing on the top of the dice is:

less than or equal to 12

Which of the following cannot be the probability of an event?

3/7

Which of the following cannot be the probability of an event?

0.82

Which of the following cannot be the probability of an event?

37%

Which of the following cannot be the probability of an event?

-2.4

If P(E) = 0.59; find P(not E)

A bag contains a certain number of red balls. A ball is drawn. Find the probability that the ball drawn is:

black

The probability that two boys do not have the same birthday is 0.897. What is the probability that the two boys have the same birthday?

A bag contains 10 red balls, 16 white balls and 8 green balls. A ball is drawn out of the bag at random. What is the probability that the ball drawn will be:

not red?

A bag contains 10 red balls, 16 white balls and 8 green balls. A ball is drawn out of the bag at random. What is the probability that the ball drawn will be:

neither red nor green?

A bag contains 10 red balls, 16 white balls and 8 green balls. A ball is drawn out of the bag at random. What is the probability that the ball drawn will be:

white or green?

A bag contains twenty Rs 5 coins, fifty Rs 2 coins and thirty Re 1 coins. If it is equally likely that one of the coins will fall down when the bag is turned upside down, what is the probability that the coin:

will be a Re 1 coin?

A bag contains twenty Rs 5 coins, fifty Rs 2 coins and thirty Re 1 coins. If it is equally likely that one of the coins will fall down when the bag is turned upside down, what is the probability that the coin:

will not be a Rs 2 coin?

A bag contains twenty Rs 5 coins, fifty Rs 2 coins and thirty Re 1 coins. If it is equally likely that one of the coins will fall down when the bag is turned upside down, what is the probability that the coin:

will neither be a Rs 5 coin nor be a Re 1 coin?

A game consists of spinning arrow which ccomes to rest pointing at one of the number 1,2,3,4,5,6,7,8,9,10,11,12; as shown below

If the outcomes are equally likely, find the probability that the pointer will point at :

(1) 6

(2) an even number

(3) a prime number

(4) a number greater than 8

(5) a number less than or equal to 9

(6) a number between 3 and 11

One card is drawn from a well shuffled deck of 52 cards. Find the probability of getting:

a queen of red color

One card is drawn from a well shuffled deck of 52 cards. Find the probability of getting:

a black face card

One card is drawn from a well shuffled deck of 52 cards. Find the probability of getting:

the jack or the queen of the hearts

One card is drawn from a well shuffled deck of 52 cards. Find the probability of getting:

a diamond

One card is drawn from a well shuffled deck of 52 cards. Find the probability of getting:

a diamond or a spade

From a deck of 52 cards, all the face cards are removed and then the remaining cards are shuffled. Now one card is drawn from the remaining deck. Find the probability that the card drawn is:

a black card

From a deck of 52 cards, all the face cards are removed and then the remaining cards are shuffled. Now one card is drawn from the remaining deck. Find the probability that the card drawn is:

8 of red color

From a deck of 52 cards, all the face cards are removed and then the remaining cards are shuffled. Now one card is drawn from the remaining deck. Find the probability that the card drawn is:

a king of black color

Seven cards:- the eight, the nine, the ten, jack, queen, king and ace of diamonds are well shuffled. One card is then picked up at random.

What is the probability that the card drawn is the eight or the king?

Seven cards:- the eight, the nine, the ten, jack, queen, king and ace of diamonds are well shuffled. One card is then picked up at random.

If the king is drawn and put aside, what is the probability that the second card picked up is:

an ace?

a king?

A box contains 150 bulbs out of which 15 are defective. It is not possible to just look at a bulb and tell whether or not it is defective. One bulb is taken out at random from this box. Calculate the probability that the bulb taken out is:

a good one

A box contains 150 bulbs out of which 15 are defective. It is not possible to just look at a bulb and tell whether or not it is defective. One bulb is taken out at random from this box. Calculate the probability that the bulb taken out is:

a defective one

4 defective pens are accidentally mixed with 16 good ones. It is not possible to just look at a pen and tell whether or not it is defective. One pen is drawn at random from the lot. What is the probability that the pen is defective?

Suppose the pen drawn in (i) is defective and is not replaced. Now one more pen is drawn at random from the rest. What is the probability that this pen is:

a) defective

b) not defective?

A bag contains 100 identical marble stones which are numbered 1 to 100. If one stone is drawn at random from the bag, find the probability that it bears:

a perfect square number

A bag contains 100 identical marble stones which are numbered 1 to 100. If one stone is drawn at random from the bag, find the probability that it bears:

a number divisible by 4

A bag contains 100 identical marble stones which are numbered 1 to 100. If one stone is drawn at random from the bag, find the probability that it bears:

a number divisible by 5

a number divisible by 4 or 5

a number divisible by 4 and 5

A circle with diameter 20 cm is drawn somewhere on a rectangular piece of paper with length 40 cm and width 30 cm. This paper is kept horizontal on table top and a die, very small in size, is dropped on the rectangular paper without seeing towards it. If the die falls and lands on paper only, find the probability that it will fall and land:

inside the circle

A circle with diameter 20 cm is drawn somewhere on a rectangular piece of paper with length 40 cm and width 30 cm. This paper is kept horizontal on table top and a die, very small in size, is dropped on the rectangular paper without seeing towards it. If the die falls and lands on paper only, find the probability that it will fall and land:

outside the circle

Two dice (each bearing numbers 1 to 6) are rolled together. Find the probability that the sum of the numbers on the upper-most faces of two dice is:

4 or 5

Two dice (each bearing numbers 1 to 6) are rolled together. Find the probability that the sum of the numbers on the upper-most faces of two dice is:

7, 8 or 9

Two dice (each bearing numbers 1 to 6) are rolled together. Find the probability that the sum of the numbers on the upper-most faces of two dice is:

between 5 and 8

more than 10

less than 6

Three coins are tossed together. Write all the possible outcomes. Now, find the probability of getting:

exactly two heads

Three coins are tossed together. Write all the possible outcomes. Now, find the probability of getting:

at least two heads

Three coins are tossed together. Write all the possible outcomes. Now, find the probability of getting:

at most two heads

Three coins are tossed together. Write all the possible outcomes. Now, find the probability of getting

all tails

at least one tail

Two dice are thrown simultaneously. What is the probability that:

4 will not come up either time?

4 will come up at least once?

Cards marked with numbers 1, 2, 3 ……… 20 are well shuffled and a card is drawn at random. What is the probability that the number on the card is:

a prime number

Cards marked with numbers 1, 2, 3 ……… 20 are well shuffled and a card is drawn at random. What is the probability that the number on the card is:

divisible by 3

Cards marked with numbers 1, 2, 3 ……… 20 are well shuffled and a card is drawn at random. What is the probability that the number on the card is:

a perfect square

Offices in Delhi are open for five days in a week (Monday to Friday). Two employees of an office remain absent for one day in the same particular week. Find the probability that they remain absent on:

the same day

Offices in Delhi are open for five days in a week (Monday to Friday). Two employees of an office remain absent for one day in the same particular week. Find the probability that they remain absent on:

consecutive day

Offices in Delhi are open for five days in a week (Monday to Friday). Two employees of an office remain absent for one day in the same particular week. Find the probability that they remain absent on:

different days

A box contains some black balls and 30 white balls. If the probability of drawing a black ball is two-fifths of a white ball, find the number of black balls in the box.

From a pack of 52 playing cards, all cards whose numbers are multiples of 3 are removed. A card is now drawn at random. What is the probability that the card drawn is

A face card (King, Jack or Queen)

From a pack of 52 playing cards, all cards whose numbers are multiples of 3 are removed. A card is now drawn at random. What is the probability that the card drawn is

An even numbered red card?