Probability — Class 11 Mathematics NCERT Solutions (Free)

Free step-by-step NCERT solutions for Class 11 Mathematics chapter "Probability" — 8 important questions with detailed answers for CBSE board exam preparation.

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TL;DR: Free step-by-step NCERT solutions for Class 11 Mathematics chapter "Probability" — 8 important questions with detailed answers for CBSE board exam pre…

Written & reviewed by the Syllab.in Academic Team (CBSE/NCERT subject experts) · Updated Jul 23, 2026

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Key Questions Covered:

A die is thrown once. Find the probability of getting (a) an even number, (b)…
Two coins are tossed simultaneously. Find the probability of getting (a) both…
A card is drawn from a standard deck of 52 cards. Find the probability of dra…
Two dice are thrown simultaneously. Find the probability that the sum of numb…
In a group of 100 students, 60 like Mathematics, 50 like Physics, and 30 like…
The probability that a student passes in Mathematics is 3/5 and in Physics is…
+ 2 more questions in the full chapter

Solutions Summary:

Question	Status
A die is thrown once. Find the probability of getting (a)…	✓ Solved
Two coins are tossed simultaneously. Find the probability…	✓ Solved
A card is drawn from a standard deck of 52 cards. Find th…	✓ Solved
Two dice are thrown simultaneously. Find the probability …	✓ Solved
In a group of 100 students, 60 like Mathematics, 50 like …	✓ Solved
The probability that a student passes in Mathematics is 3…	✓ Solved

Showing 6 of 8 questions

Q1: A die is thrown once. Find the probability of getting (a) an even number, (b) a number greater than 4.

When a die is thrown once, possible outcomes: {1, 2, 3, 4, 5, 6} Total possible outcomes = 6 (a) Find probability of getting an even number: Favourable outcomes: {2, 4, 6} Number of favourable outcomes = 3 P(even) = 3/6 = 1/2 (b) Find probability of getting a number greater than 4: Favourable outcomes: {5, 6} Number of favourable outcomes = 2 P(greater than 4) = 2/6 = 1/3 Final Answer: (a) P(even) = 1/2, (b) P(>4) = 1/3

Q2: Two coins are tossed simultaneously. Find the probability of getting (a) both heads, (b) at least one tail.

When two coins are tossed, possible outcomes: {HH, HT, TH, TT} Total possible outcomes = 4 (a) Find probability of both heads: Favourable outcomes: {HH} Number of favourable outcomes = 1 P(both heads) = 1/4 (b) Find probability of at least one tail: Favourable outcomes: {HT, TH, TT} Number of favourable outcomes = 3 P(at least one tail) = 3/4 Alternatively: P(at least one tail) = 1 - P(both heads) = 1 - 1/4 = 3/4 Final Answer: (a) P(both heads) = 1/4, (b) P(at least one tail) = 3/4

Q3: A card is drawn from a standard deck of 52 cards. Find the probability of drawing (a) a king, (b) a red card, (c) a diamond.

A standard deck has 52 cards with 4 kings, 26 red cards, and 13 diamonds. (a) Probability of drawing a king: Number of kings = 4 P(king) = 4/52 = 1/13 (b) Probability of drawing a red card: Number of red cards = 26 P(red) = 26/52 = 1/2 (c) Probability of drawing a diamond: Number of diamonds = 13 P(diamond) = 13/52 = 1/4 Final Answer: (a) P(king) = 1/13, (b) P(red) = 1/2, (c) P(diamond) = 1/4

Q4: Two dice are thrown simultaneously. Find the probability that the sum of numbers is (a) 7, (b) greater than 10.

When two dice are thrown, total possible outcomes = 6 × 6 = 36 (a) Find probability that sum = 7: Favourable outcomes: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) Number of favourable outcomes = 6 P(sum = 7) = 6/36 = 1/6 (b) Find probability that sum > 10: For sum > 10, we need sum = 11 or 12 Sum = 11: (5,6), (6,5) → 2 outcomes Sum = 12: (6,6) → 1 outcome Number of favourable outcomes = 2 + 1 = 3 P(sum > 10) = 3/36 = 1/12 Final Answer: (a) P(sum = 7) = 1/6, (b) P(sum > 10) = 1/12

Q5: In a group of 100 students, 60 like Mathematics, 50 like Physics, and 30 like both subjects. A student is selected at random. Find the probability that the student likes (a) Mathematics or Physics, (b) neither subject.

Given: Total students = 100 M = students who like Mathematics = 60 P = students who like Physics = 50 M ∩ P = students who like both = 30 Step 1: Use the formula: M ∪ P = M + P - (M ∩ P) M ∪ P = 60 + 50 - 30 = 80 (a) Probability of liking Mathematics or Physics: P(M ∪ P) = 80/100 = 4/5 (b) Probability of liking neither subject: Students who like neither = Total - (M ∪ P) = 100 - 80 = 20 P(neither) = 20/100 = 1/5 Alternatively: P(neither) = 1 - P(M ∪ P) = 1 - 4/5 = 1/5 Final Answer: (a) P(M ...

Q6: The probability that a student passes in Mathematics is 3/5 and in Physics is 2/5. Assuming independence, find the probability that the student passes (a) both subjects, (b) at least one subject.

Given: P(M) = 3/5 and P(P) = 2/5 (independent events) (a) Find probability of passing both subjects: Since events are independent: P(M ∩ P) = P(M) × P(P) P(M ∩ P) = (3/5) × (2/5) = 6/25 (b) Find probability of passing at least one subject: P(at least one) = P(M ∪ P) = P(M) + P(P) - P(M ∩ P) = 3/5 + 2/5 - 6/25 = 15/25 + 10/25 - 6/25 = 19/25 Alternatively: P(at least one) = 1 - P(fail both) = 1 - [P(not M) × P(not P)] = 1 - [(2/5) × (3/5)] = 1 - 6/25 = 19/25 Final Answer: (a) P(both) = 6/25, (...

Showing 6 of 8 questions. Visit the full page for complete solutions.