Class 11 Maths Chapter 14 Probability – Extra Questions with Answers

Working out a probability starts with listing every possible outcome, the sample space, and then counting the ones that count as a success. These Class 11 Maths Chapter 14 questions cover sample spaces, complementary events, and mutually exclusive outcomes using dice and similar examples.

Last Updated: September 23, 2026

Very Short Answer Questions (1 mark)

Q1. Write the sample space when a die is rolled.
Ans: {1, 2, 3, 4, 5, 6}.

Q2. What is the probability of a sure event?
Ans: 1.

Q3. Find the probability of getting an even number when a die is rolled.
Ans: Favourable outcomes {2,4,6} = 3; P = 3/6 = 1/2.

Q4. If P(A) = 0.4, find P(A’), the complement.
Ans: 1−0.4 = 0.6.

Q5. Are the events “rolling an even number” and “rolling an odd number” on a die mutually exclusive?
Ans: Yes, they cannot happen simultaneously.

Short Answer Questions (2–3 marks)

Q6. A card is drawn from a standard deck of 52 cards. Find the probability that it is a king or a queen.
Ans: These are mutually exclusive events. P(king) = 4/52; P(queen) = 4/52. P(king or queen) = 4/52 + 4/52 = 8/52 = 2/13.

Q7. Two dice are rolled. Find the probability that the sum of the numbers is 7.
Ans: Total outcomes = 36. Favourable: (1,6),(2,5),(3,4),(4,3),(5,2),(6,1) = 6 outcomes. P = 6/36 = 1/6.

Q8. In a class of 40 students, 18 play cricket, 20 play football, and 8 play both. Find the probability that a randomly chosen student plays cricket or football, using the addition rule.
Ans: P(cricket) = 18/40, P(football) = 20/40, P(both) = 8/40. P(cricket or football) = 18/40 + 20/40 − 8/40 = 30/40 = 3/4.

Higher-Order Thinking / Application Questions

Q9. Explain why the formula P(A∪B) = P(A) + P(B) would overcount the probability if A and B are NOT mutually exclusive, using the class example above (cricket/football) as illustration.
Ans: If we simply added P(cricket)+P(football) = 18/40+20/40 = 38/40 without subtracting the overlap, we would be double-counting the 8 students who play both sports (they’d be counted once in the cricket group and again in the football group). Subtracting P(A∩B) = 8/40 removes this double-counting, correctly giving 30/40 as the true probability of playing at least one sport.

Q10. A single die is rolled once. Event A = “rolling a number greater than 4” and Event B = “rolling an even number.” Find P(A), P(B), P(A∩B), and P(A∪B), explaining each step.
Ans: A = {5,6}, so P(A) = 2/6 = 1/3. B = {2,4,6}, so P(B) = 3/6 = 1/2. A∩B (both greater than 4 AND even) = {6}, so P(A∩B) = 1/6. Using the addition rule: P(A∪B) = P(A)+P(B)−P(A∩B) = 1/3+1/2−1/6 = 2/6+3/6−1/6 = 4/6 = 2/3.

Frequently Asked Questions

If two dice are rolled, what is the probability of getting a sum of 8?
There are 5 favorable outcomes out of 36 total outcomes, so the probability is 5 over 36.

A bag has 4 red and 6 black balls, what is the probability of drawing one ball that is red?
There are 4 favorable outcomes out of 10 total balls, so the probability is 4 over 10, which simplifies to 2 over 5.

Written by Satish

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