Probability

CBSE Class 10 — Maths — Previous Year Questions

68 questions104 total marksVSA: 18MCQ: 27Case-Study: 15Assertion-Reason: 2SA: 6

Q1.VSA1 mark(2020)Easy

A letter of English alphabet is chosen at random. What is the probability that the chosen letter is a consonant?

Q2.VSA1 mark(2020)Easy

A die is thrown once. What is the probability of getting a number less than

3

Q3.VSA1 mark(2020)Easy

If the probability of winning a game is

0.07

, what is the probability of losing it?

Q4.VSA1 mark(2020)Easy

If a number

x

is chosen at random from the numbers

- 3, - 2, - 1, 0, 1, 2, 3

, then find the probability of

x^{2} < 4

Q5.VSA1 mark(2020)Medium

What is the probability that a randomly taken leap year has 52 Sundays?

Q6.VSA1 mark(2020)Easy

A die is thrown once. What is the probability of getting a prime number.

Q7.VSA1 mark(2020)Easy

The probability that it will rain tomorrow is 0.85. What is the probability that it will not rain tomorrow?

Q8.MCQ1 mark(2020)Easy

A bag contains 3 red, 5 black and 7 white balls. A ball is drawn from the bag at random. The probability that the drawn is not black, is

Q9.VSA1 mark(2020)Easy

Two dice are thrown simultaneously. What is the probability that the sum of the two numbers appearing on the top is 13?

Q10.MCQ1 mark(2020)Easy

The probability of an event that is sure to happen, is ________.

Q11.MCQ1 mark(2023)Easy

Probability of happening of an event is denoted by

p

and probability of non-happening of the event is denoted by

q

. Relation between

p

and

q

is
(A)

p + q = 1

(B)

p = 1, q = 1

(C)

p = q - 1

(D)

p + q + 1 = 0

Q12.MCQ1 mark(2023)Easy

A girl calculates that the probability of her winning the first prize in a lottery is

0.08

. If 6000 tickets are sold, how many tickets has she bought?
(A)

40

(B)

240

(C)

480

(D)

750

Q13.MCQ1 mark(2023)Easy

In a group of 20 people, 5 can't swim. If one person is selected at random, then the probability that he/she can swim, is
(A)

\frac{3}{4}

(B)

\frac{1}{3}

(C)

1

(D)

\frac{1}{4}

Q14.MCQ1 mark(2023)Easy

A bag contains 100 cards numbered 1 to 100. A card is drawn at random from the bag. What is the probability that the number on the card is a perfect cube?
(a)

\frac{1}{20}

(b)

\frac{3}{50}

(c)

\frac{1}{25}

(d)

\frac{7}{100}

Q15.MCQ1 mark(2023)Easy

If three coins are tossed simultaneously, what is the probability of getting at most one tail?
(a)

\frac{3}{8}

(b)

\frac{4}{8}

(c)

\frac{5}{8}

(d)

\frac{7}{8}

Q16.Case-Study1 mark(2023)Easy

Case Study - 3

Computer-based learning (CBL) refers to any teaching methodology that makes use of computers for information transmission. At an elementary school level, computer applications can be used to display multimedia lesson plans. A survey was done on 1000 elementary and secondary schools of Assam and they were classified by the number of computers they had.

$Computer lab classroom$

| Number of Computers |

1 - 10

11 - 20

21 - 50

51 - 100

101

and more |
|---|---|---|---|---|---|
| Number of Schools |

250

200

290

180

80

|

One school is chosen at random. Then:

(i) Find the probability that the school chosen at random has more than 100 computers.

Q17.Case-Study1 mark(2023)Easy

Case Study - 3 (continued)

Refer to the survey data in Q38.

(iii) Find the probability that the school chosen at random has 10 or less than 10 computers.

Q18.MCQ1 mark(2023)Easy

Two dice are thrown together. The probability of getting the difference of numbers on their upper faces equals to 3 is:

Q19.MCQ1 mark(2023)Easy

A card is drawn at random from a well-shuffled pack of 52 cards. The probability that the card drawn is not an ace is:

Q20.Assertion-Reason1 mark(2023)Medium

Assertion (A): The probability that a leap year has 53 Sundays is

\frac{2}{7}

.

Reason (R): The probability that a non-leap year has 53 Sundays is

\frac{5}{7}

Q21.MCQ1 mark(2023)Easy

Two coins are tossed together. The probability of getting at least one tail is:

Q22.MCQ1 mark(2023)Easy

Which of the following numbers **cannot** be the probability of happening of an event?

Q23.Case-Study1 mark(2023)Easy

A middle school decided to run the following spinner game as a fund-raiser on Christmas Carnival.

$Spinners I and II$

**Making Purple:** Spin each spinner once. Blue and red make purple. So, if one spinner shows Red (R) and another Blue (B), then you 'win'. One such outcome is written as 'RB'.

Based on the above, answer the following questions:

(i) List all possible outcomes of the game.

Q24.Case-Study1 mark(2023)Easy

(ii) Find the probability of 'Making Purple'.

Q25.MCQ1 mark(2023)Easy

A bag contains

5

pink,

8

blue and

7

yellow balls. One ball is drawn at random from the bag. What is the probability of getting neither a blue nor a pink ball?

Q26.MCQ1 mark(2023)Easy

A card is drawn at random from a well shuffled deck of

52

playing cards. The probability of getting a face card is

Q27.Case-Study1 mark(2023)Easy

"Eight Ball" is a game played on a pool table with

15

balls numbered

1

15

and a "cue ball" that is solid and white. Of the

15

numbered balls, eight are solid (non-white) coloured and numbered

1

8

and seven are striped balls numbered

9

15

.

$Pool balls on a table$

The

15

numbered pool balls (no cue ball) are placed in a large bowl and mixed, then one ball is drawn out at random.

Based on the above information, answer the following questions:

(i) What is the probability that the drawn ball bears number

8

Q28.Case-Study1 mark(2023)Easy

(ii) What is the probability that the drawn ball bears an even number?

Q29.Case-Study1 mark(2023)Easy

(ii) What is the probability that the drawn ball bears a number, which is a multiple of

3

Q30.MCQ1 mark(2024)Easy

If the probability of a player winning a game is

0.79

, then the probability of his losing the same game is:

Q31.MCQ1 mark(2024)Easy

From the data

1, 4, 7, 9, 16, 21, 25

, if all the even numbers are removed, then the probability of getting at random a prime number from the remaining is:

Q32.MCQ1 mark(2024)Easy

Two dice are rolled together. The probability of getting sum of numbers on the two dice as

2

3

5

, is:

Q33.MCQ1 mark(2024)Easy

Two dice are rolled together. The probability of getting the sum of the two numbers to be more than 10, is

Q34.MCQ1 mark(2024)Easy

A box contains cards numbered

6

55

. A card is drawn at random from the box. The probability that the drawn card has a number which is a perfect square, is

Q35.MCQ1 mark(2024)Easy

Two dice are tossed simultaneously. The probability of getting odd numbers on both the dice is:

Q36.MCQ1 mark(2024)Easy

For an event

E

, if

P (E) + P (\overset{ˉ}{E}) = q

, then the value of

q^{2} - 4

is:

Q37.MCQ1 mark(2024)Easy

One ticket is drawn at random from a bag containing tickets numbered 1 to 40. The probability that the selected ticket has a number which is a multiple of 7 is:

Q38.MCQ1 mark(2025)Easy

A card is selected at random from a deck of 52 playing cards. The probability of it being a red face card is:

Q39.Assertion-Reason1 mark(2025)Easy

Assertion (A): The probability of selecting a number at random from the numbers 1 to 20 is 1.

Reason (R): For any event E, if

P (E) = 1

, then E is called a sure event.

Q40.MCQ1 mark(2025)Easy

The probability of drawing an even prime number out of numbers from 1 to 30 is:

Q41.MCQ1 mark(2025)Easy

In a cricket match, a batsman hits the boundary 7 times out of the 42 balls he plays. The probability of his *not* hitting a boundary is:

Q42.MCQ1 mark(2025)Easy

A die is thrown once. The probability of getting a number which is *not* a factor of 36, is:

Q43.MCQ1 mark(2025)Easy

The number of red balls in a bag is 10 more than the number of black balls. If the probability of drawing a red ball at random from this bag is

\frac{3}{5}

, then the total number of balls in the bag is:

Q44.MCQ1 mark(2025)Easy

A pair of dice is thrown. The probability that sum of numbers appearing on top faces is at most 10 is:

Q45.VSA2 marks(2020)Easy

If a number

x

is chosen at random from the numbers

- 3, - 2, - 1, 0, 1, 2, 3

. What is the probability that

x^{2} \leq 4

Q46.VSA2 marks(2020)Easy

A child has a die whose six faces show the letters as shown below:

| A | B | C | D | E | A |

The die is thrown once. What is the probability of getting (i) A, (ii) D?

Q47.VSA2 marks(2020)Medium

Find the probability that a leap year selected at random will contain 53 Sundays and 53 Mondays.

Q48.VSA2 marks(2020)Easy

Tree Plantation Drive

A group Housing Society has 600 members, who have their houses in the campus and decided to hold a Tree Plantation Drive on the occasion of New Year. Each household was given the choice of planting a sampling of its choice. The number of different types of samplings planted were:

(i) Neem - 125
(ii) Peepal - 165
(iii) Creepers - 50
(iv) Fruit plants - 150
(v) Flowering plants - 110

On the opening ceremony, one of the plants is selected randomly for a prize. After reading the above passage, answer the following questions:

What is the probability that the selected plant is
(i) A fruit plant or a flowering plant?
(ii) Either a Neem plant or a Peepal plant?

Q49.VSA2 marks(2023)Easy

A bag contains 4 red, 3 blue and 2 yellow balls. One ball is drawn at random from the bag. Find the probability that drawn ball is
(i) red
(ii) yellow.

Q50.Case-Study2 marks(2023)Easy

Case Study - 3 (continued)

Refer to the survey data in Q38.

(ii)(a) Find the probability that the school chosen at random has 50 or fewer computers.

Q51.Case-Study2 marks(2023)Easy

Case Study - 3 (continued)

Refer to the survey data in Q38.

(ii)(b) Find the probability that the school chosen at random has no more than 20 computers.

Q52.VSA2 marks(2023)Easy

If a fair coin is tossed twice, find the probability of getting 'atmost one head'.

Q53.Case-Study2 marks(2023)Medium

(iii) (a) For each win, a participant gets ₹

10

, but if he/she loses, he/she has to pay ₹

5

to the school. If

99

participants played, calculate how much fund could the school have collecting.

Q54.Case-Study2 marks(2023)Medium

(iii) (b) If the same amount of ₹

5

has been decided for winning or losing the game, then how much fund had been collected by school? (Number of participants

= 99

)

Q55.Case-Study2 marks(2023)Easy

(iii) What is the probability that the drawn ball is a solid coloured and bears an even number?

Q56.VSA2 marks(2024)Easy

In a pack of 52 playing cards one card is lost. From the remaining cards, a card is drawn at random. Find the probability that the drawn card is queen of heart, if the lost card is a black card.

Q57.VSA2 marks(2024)Easy

A carton consists of 60 shirts of which 48 are good, 8 have major defects and 4 have minor defects. Nigam, a trader, will accept the shirts which are good but Anmol, another trader, will only reject the shirts which have major defects. One shirt is drawn at random from the carton. Find the probability that it is acceptable to Anmol.

Q58.VSA2 marks(2025)Easy

The probability of guessing the correct answer of a certain test question is

\frac{x}{12}

. If the probability of not guessing the correct answer is

\frac{5}{6}

, then find the value of

x

Q59.VSA2 marks(2025)Easy

Two friends Anil and Ashraf were born in the December month in the year 2010. Find the probability that:
(i) they share same date of birth.
(ii) they have different dates of birth.

Q60.SA3 marks(2020)Medium

Read the following passage and answer the questions given at the end:

**Diwali Fair**

A game in booth at Diwali fair involves using of spinner first. Then, if the spinner stops at an even number, the player is allowed to pick a marble from bag. The spinner and the marbles in the bag are represented in Figure 8.

$Spinner with numbers 1, 2, 4, 6, 8, 10 and a bag with black and white marbles$

Prizes are given, when a black marble is picked. Shweta plays the game once.

(i) What is the probability that she will be allowed to pick a marble from the bag?

(ii) Suppose she is allowed to pick a marble from the bag, what is the probability of getting a prize, when it is given that the bag contains

20

balls out of which

6

are black?

Q61.SA3 marks(2024)Medium

Three coins are tossed simultaneously. What is the probability of getting
(i) at least one head?
(ii) exactly two tails?
(iii) at most one tail?

Q62.SA3 marks(2024)Medium

A box contains

90

discs which are numbered

1

90

. If one disc is drawn at random from the box, find the probability that it bears a:
(i)

2

-digit number less than

40

.
(ii) number divisible by

5

and greater than

50

.
(iii) a perfect square number.

Q63.SA3 marks(2024)Medium

Three unbiased coins are tossed simultaneously. Find the probability of getting:
(i) at least one head.
(ii) exactly one tail.
(iii) two heads and one tail.

Q64.SA3 marks(2025)Medium

Two dice are thrown at the same time. Determine the probability that the difference of the numbers on the two dice is 2.

Q65.SA3 marks(2025)Easy

Three unbiased coins are tossed simultaneously. Find the probability of getting:
(a) exactly two tails
(b) at least one head
(c) at most two heads

Q66.Case-Study4 marks(2024)Medium

In a survey on holidays,

120

people were asked to state which type of transport they used on their last holiday. The following pie chart shows the results of the survey.

$Pie chart showing transport survey results$

Observe the pie chart and answer the following questions:
(i) If one person is selected at random, find the probability that he/she travelled by bus or ship.
(ii) Which is most favourite mode of transport and how many people used it?
(iii) (a) A person is selected at random. If the probability that he did not use train is

\frac{4}{5}

, find the number of people who used train.

**OR**

(iii) (b) The probability that randomly selected person used aeroplane is

\frac{7}{60}

. Find the revenue collected by air company at the rate of ₹

5, 000

per person.

Q67.Case-Study4 marks(2024)Medium

In a survey on holidays,

120

people were asked to state which type of transport they used on their last holiday. The following pie chart shows the results of the survey.

$Pie chart showing transport survey results$

Observe the pie chart and answer the following questions:
(i) If one person is selected at random, find the probability that he/she travelled by bus or ship.
(ii) Which is most favourite mode of transport and how many people used it?
(iii) (b) The probability that randomly selected person used aeroplane is

\frac{7}{60}

. Find the revenue collected by air company at the rate of ₹

5, 000

per person.

Q68.Case-Study4 marks(2025)Medium

**Case Study - 2**

Rahul is a lucky charm for his cricket team. He has a jar of cards with numbers from 10 to 74. Before each match, he draws a card from the jar. If the card bears an even number, the team wins. If the number is even and divisible by 5, they win by a big margin. If the number is an odd number less than 30, they win by a small margin. And if the number is a prime number between 50 and 74, they lose.

$Jar of numbered cards$

Answer the following questions if Rahul draws a card today:

(i) What is the probability that Rahul draws a card with an even number?

(ii) What is the probability that Rahul draws a card with an odd number less than 30?

(iii) (a) What is the probability that Rahul draws a card with a prime number between 50 and 74?

**OR**

(iii) (b) What is the probability that Rahul draws a card with an even number divisible by 5?

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