WORKSHEET

DEPT. OF ACADEMICS

Campus GIIS, Whitefield Session 2025 - 2026

Topic Probability Work Sheet No. 3

Class X Subject Mathematics

Name Date

SECTION – A
1. There is a square board of side ‘2a’ units circumscribing a yellow circle. Jayadev is asked to keep a
dot on the above said board. The probability that he keeps the dot on the shaded region is:
(a) π/4 (b) (4 − π) /4 (c) (π − 4) /4 (d) 4/π

2. If a card is drawn from a deck of cards, what is the probability of a card drawn to be a red or a black
card and what can we say about that event?
(a) 1 and it is a sure event. (b) 0 and it is a sure event.
(c) 1 and it is an impossible event. (d) 0 and it is an impossible event.

3. In an MCQ test, a student guesses the correct answer x out of y times. If the probability that the
student guesses the answer to be wrong is 2/3 then what is the relation between x and y
(a) y = 3x (b) x = 3y (c) 3x = 2y (d) 2x = 3y

4. If a letter is chosen at random from the letters of English alphabets, then the probability that it is a
letter of the word ‘MATHEMATICS’ is:
(a) 4/13 (b) 9/26 (c) 5/13 (d) 11/26

5. Cards numbered 7 to 40 were put in a box. Anish selects a card at random. What is the probability
that the selected card is a multiple of 7?
(a) 7/34 (b) 5/34 (c) 6/35 (d) 7/35

6. A bowl contains 3 red and 2 blue marbles.

Roohi wants to pick a red marble. Which of the following changes could she make so that the
probability of picking a red marble is greater than it was before?
i) Adding a red marble ii) Removing a blue marble
iii) Adding 1 red and 1 blue marble
(a) Only (i) (b) Only (i) and (ii) (c) Only (i) and (iii) (d) All of the above

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7. A dice is thrown twice. The probability of getting 4, 5 or 6 in the first throw and 1, 2, 3 or 4 in the
second throw is:
(a) 1/3 (b) 2/3 (c) 1/2 (d) 1/4

8. A school has five houses A, B, C, D and E. A class has 23 students, 4 from house A, 8 from house B,
5 from house C, 2 from house D and the rest from house E. A single student is selected at random to
be the class monitor. The probability that the selected student is not from houses A, B and C is:
(a) 4/23 (b) 6/23 (c) 8/23 (d) 17/23

In the following questions 9 and 10, a statement of assertion (A) is followed by a statement of
reason (R). Mark the correct choice as:
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.
9. Assertion (A): The probability that a leap year has 53 Sundays is 2/7.
Reason (R): The probability that a non–leap year has 53 Sundays is 5/7.

10. Assertion (A): The probability of getting a bad egg in a lot of 400 is 0.035. The number of good
eggs in the lot is 386.
Reason (R): If the probability of an event is p, the probability of its complementary event will be
1 – p.

SECTION – B
11.Cards, marked with numbers 5 to 50, are placed in a box and mixed thoroughly. A card is drawn
from the box at random. Find the probability that the number on the taken card is
(i) a prime number less than 10. (ii) a number which is a perfect square.

12.The king, queen and jack of diamonds are removed from a pack of 52 cards and then the pack is well
shuffled. A card is drawn from the remaining cards. Find the probability of getting a card of

(i) diamonds, (ii) a jack

13.Two different dice are tossed together. Find the probability

(i) that the number on each dice is even
(ii) that the sum of numbers appearing on two dice is 5.

14.Find the probability that a leap year should have exactly 52 tuesday.

SECTION – C
15.A bag contains 12 balls out of which x are white.
i) If one ball is drawn at random, what is the probability that it will be a white ball?
ii) If 6 more white balls are put in the bag, the probability of drawing a white ball will be double
than that in (i). Find x.

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16.One card is drawn from a well shuffled deck of 52 cards. Find the probability of getting
(i) a face card or a black card
(ii) neither an ace nor a king
(iii) a jack and a black card.

17.Two different dice are thrown together. Find the probability that the numbers obtained:
(a) have a sum less than 7
(b) have a product less than 16
(c) is a doublet of odd numbers.

SECTION – D

18.From a pack of 52 playing cards, Jacks and Kings of red colour and Queens and Aces of black colour
are removed. The remaining cards are mixed and a card is drawn at random. Find the probability that the
drawn card is:
(a) a black queen.
(b) a card of red colour.
(c) a Jack of black colour.
(d) a face card.

SECTION – E
(Case Study Based Questions)

19.A school offers several sports to its students such as cricket, football, basketball, tennis, badminton
and swimming. Based on past records, the sports teacher prepared a pie chart as shown below showing
preference of students towards a particular sport.

(a) Find the probability of favourite sport being either swimming or badminton.
(b) Find the probability of favourite sport being neither football nor cricket.
(c) Find the probability of favourite sport being basketball, tennis or cricket.

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DEPT. OF ACADEMICS

20.Two friends are travelling in a bus. They were feeling bored, so they started playing a game with a
pair of dice that one of them had. Each of them started rolling the pair of dice one by one, stating one
condition before rolling. If the person gets the numbers according to the condition stated by him, he wins
and get a score.

Based on the above information, answer the following questions.

i)(a) First friend says, “a doublet”. What is the probability of his winning?
(b) Second friend says, ‘‘sum less than 9’’. What is the probability of his winning?

ii)(a) First one says, “6 will come up either time.” What is the probability of his winning?
(b) Second one says, “sum is an even number”. What is the probability of his losing?

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