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CBSE · Class 11 · Mathematics

Probability

Standard difficulty · 20 questions · 40 marks

Name: Date: Score: ____ / 40

Show your working for Sections B and C. Answers are on the last page — try every question first!

Section A — Choose the correct answer8 × 1 = 8 marks
1.
How many outcomes are in the sample space when a coin is tossed 4 times?
  1. 8
  2. 32
  3. 22
  4. 16
2.
If P(A) = 19/40, P(B) = 11/20 and P(A ∩ B) = 1/4, then P(A ∪ B) is:
  1. 31/40
  2. 41/40
  3. 51/40
  4. 209/800
3.
If P(A) = 1/9, then P(not A) is:
  1. 1/18
  2. 1/8
  3. 4/9
  4. 8/9
4.
A die is thrown. A: getting an odd number; B: getting a number greater than 4. Events A and B are:
  1. exhaustive but not mutually exclusive
  2. mutually exclusive and exhaustive
  3. mutually exclusive but not exhaustive
  4. neither mutually exclusive nor exhaustive
5.
The set of all possible outcomes of a random experiment is called the:
  1. trial
  2. event
  3. sample space
  4. probability
6.
Two dice are thrown. The probability that the sum is greater than 6 is:
  1. 11/18
  2. 7/12
  3. 7/4
  4. 5/12
7.
A card is drawn from a pack of 52. The probability that it is an ace or a black card is:
  1. 1/2
  2. 15/26
  3. 1/26
  4. 7/13
8.
Assertion (A): If P(A) = 3/10, P(B) = 1/2 and P(A ∩ B) = 1/5, then P(A ∪ B) = 3/5.
Reason (R): P(A ∪ B) = P(A) + P(B) for any two events.
  1. Both A and R are true, and R is the correct explanation of A.
  2. Both A and R are true, but R is not the correct explanation of A.
  3. A is true, but R is false.
  4. A is false, but R is true.
Section B — Short answer8 × 2 = 16 marks
9.
A coin is tossed three times. Write the sample space. What is the probability of more tails than heads?
10.
If P(A) = 3/10, P(A ∩ B) = 1/10 and P(A ∪ B) = 17/30, find P(B).
11.
A die is thrown. A: an odd number; B: a factor of 6. Find A ∪ B, A ∩ B and A′, and their probabilities.
12.
A committee of 3 is chosen at random from 7 men and 7 women. What is the probability that all of them are women?
13.
3 cards are drawn at random from a pack of 52. What is the probability that all of them are aces?
14.
In a class, 57% of students passed in Mathematics, 51% in English and 21% in both. What percentage passed in at least one subject? What percentage failed in both? What is the probability that a student chosen at random passed in exactly one?
15.
Two dice are thrown. Find the probability that the first die shows more than the second.
16.
A coin is tossed 5 times. Find the probability of (a) at least one tail, (b) no tail.
Section C — Word problems4 × 4 = 16 marks
17.
A team of 3 is chosen at random from 8 boys and 7 girls. Find the probability that the team has (a) exactly one girl, (b) no girls, (c) at least one girl.
18.
Two dice are thrown. A: the sum is 6; B: the first die shows more than 4. Find P(A), P(B), P(A ∩ B) and P(A ∪ B). Are A and B mutually exclusive?
19.
2 cards are drawn at random from a pack of 52. Find the probability that (a) all are hearts, (b) all are number cards (2 to 10), (c) none is a jack.
20.
In a survey of 75 people, 44 read newspaper H, 28 read newspaper T and 9 read both. A person is chosen at random. Find the probability that the person reads (a) at least one newspaper, (b) neither, (c) exactly one, (d) H but not T.
AmbifulWorksheets
Practice that never repeats
CBSE · Class 11 · Mathematics

Answer key

Probability · AW-11M-PB1-2026-V1 · For parents — fold back or tear off before handing the sheet to your child.

QAnswerWorking
1(d) 16—
2(a) 31/40P(A) + P(B) − P(A ∩ B)
3(d) 8/91 − P(A)
4(d) neither mutually exclusive nor exhaustiveA = {1, 3, 5}, B = {5, 6}
5(c) sample space—
6(b) 7/1221 favourable outcomes out of 36
7(d) 7/13(4 + 26 − 2) ÷ 52
8(c) A is true, but R is false.A is true: 3/10 + 1/2 − 1/5 = 3/5. R is false.
9S = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}; 1/2—
1011/30P(A ∪ B) = P(A) + P(B) − P(A ∩ B)
11A ∪ B = {1, 2, 3, 5, 6} (5/6); A ∩ B = {1, 3} (1/3); A′ = {2, 4, 6} (1/2)A = {1, 3, 5}, B = {1, 2, 3, 6}
125/52C(7, 3) ÷ C(14, 3) = 35 ÷ 364
131/5525C(4, 3) ÷ C(52, 3) = 4 ÷ 22,100
1487%; 13%; 33/50P(M ∪ E) = P(M) + P(E) − P(M ∩ E)
155/1215 of the 36 outcomes
16(a) 31/32; (b) 1/32P(no tail) = (1/2)5; at least one = 1 − that
17(a) 28/65; (b) 8/65; (c) 57/65total C(15, 3) = 455
18P(A) = 5/36, P(B) = 1/3, P(A ∩ B) = 1/36, P(A ∪ B) = 4/9; not mutually exclusiveA ∩ B = {(5, 1)}
19(a) 1/17; (b) 105/221; (c) 188/221total C(52, 2) = 1,326
20(a) 21/25; (b) 4/25; (c) 18/25; (d) 7/15n(H ∪ T) = 44 + 28 − 9 = 63