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Probability – Class 11 Mathematics notes, important questions and MCQs

NCERT Class 11 Mathematics, chapter 14. Notes, key terms, important questions with answers and MCQs.

Chapter overview

Probability measures how likely an event is. The axiomatic approach uses sample spaces and events, with rules for unions and complements.

Basics

Sample space S = set of all outcomes; an event is a subset of S.
P(E) = favourable outcomes/total outcomes for equally likely outcomes; 0 ≤ P(E) ≤ 1.
P(not E) = 1 − P(E).

Events

Mutually exclusive: A ∩ B = ∅; exhaustive: A ∪ B = S.
P(A ∪ B) = P(A) + P(B) − P(A ∩ B).
Tossing two coins gives 4 outcomes; throwing two dice gives 36.

Key terms

Sample space: set of all possible outcomes
Mutually exclusive events: events that cannot happen together
Exhaustive events: events whose union is the whole sample space, so at least one must occur

Formulas

P(A ∪ B) = P(A) + P(B) − P(A ∩ B)
P(E′) = 1 − P(E)

Important questions with answers

Write the sample space when a coin is tossed three times.2 marks

{HHH, HHT, HTH, THH, HTT, THT, TTH, TTT} — 8 outcomes.

From a bag with 5 red and 3 black balls, 2 balls are drawn at random. Find P(both red).3 marks

Total ways = ⁸C₂ = 28; favourable = ⁵C₂ = 10. P = 10/28 = 5/14.

A committee of 4 is chosen at random from 5 boys and 4 girls. Find the probability that it has (i) exactly 2 girls, (ii) at least one girl.5 marks

Total = ⁹C₄ = 126. (i) ⁴C₂ × ⁵C₂ = 6 × 10 = 60, so P = 60/126 = 10/21. (ii) P(no girl) = ⁵C₄/126 = 5/126, so P(at least one girl) = 1 − 5/126 = 121/126.

Quick revision

Probability lies between 0 and 1.
Two dice: 36 outcomes.
Sum of probabilities of all outcomes = 1.

Exam tips

For "at least one", use 1 − P(none).
For "at least one" or "none" type problems, use the complement: P(at least one) = 1 − P(none).

Practice MCQs

Probability of getting a head in one toss is
1. ½
2. 0
3. 1
4. ¼
Show answer
Answer: (a) ½. 1 of 2.
Probability of an impossible event is
1. 0
2. 1
3. ½
4. −1
Show answer
Answer: (a) 0. Zero.
Probability of getting a sum of 7 with two dice is
1. 1/6
2. 1/12
3. 7/36
4. 1/36
Show answer
Answer: (a) 1/6. 6/36.
If P(A) = 0.4, P(B) = 0.5 and P(A ∩ B) = 0.2, then P(A ∪ B) is
1. 0.9
2. 0.1
3. 0.2
4. 0.7
Show answer
Answer: (d) 0.7. 0.4 + 0.5 − 0.2.
A card is drawn from 52 cards. P(a face card) is
1. 3/13
2. 4/13
3. 1/13
4. 12/13
Show answer
Answer: (a) 3/13. 12/52.
Probability of at least one head in 3 tosses is
1. 1/8
2. 3/8
3. 7/8
4. ½
Show answer
Answer: (c) 7/8. 1 − 1/8.
A card is drawn from a pack of 52. Probability that it is a king or a heart is
1. 17/52
2. 3/13
3. 1/4
4. 4/13
Show answer
Answer: (d) 4/13. (4 + 13 − 1)/52 = 4/13.
Two dice are thrown. P(product of numbers is even) is
1. 3/4
2. 1/2
3. 1/4
4. 2/3
Show answer
Answer: (a) 3/4. 1 − P(both odd) = 1 − 9/36.

All chapters of Class 11 Mathematics

Written by Kundali IQ from standard, well-established facts to help with revision. This is not an official NCERT publication; always read your textbook too.