Mathematics · Class 10
Probability
Classical probability, events, and complementary events.
3 sections15–25 min read6 MCQs · 2 examples
Chapter Overview
P(E) = Number of favourable outcomes / Total number of equally likely outcomes. Always check that outcomes are equally likely before using classical probability.
Probability measures likelihood of events on a scale from 0 to 1. Class 10 uses the classical (theoretical) definition for equally likely outcomes — coins, dice, cards, and bags of balls.
Classical Probability
Probability
P(E) = n(E) / n(S)
Complement
P(not E) = 1 − P(E)
Sure event
P(S) = 1
Impossible event
P(∅) = 0
Event Types
- Elementary event: single outcome
- Complementary events: E and not E exhaust sample space
- Sum of probabilities of all elementary events = 1
- Probability cannot be negative or greater than 1
Solved Examples
Step-by-step solutions — read each step before checking the final answer.
Example 1: Die roll
A fair die is rolled. Find P(getting an even number).
- 1S = {1,2,3,4,5,6}, n(S) = 6
- 2E = {2,4,6}, n(E) = 3
- 3P(E) = 3/6 = 1/2
Answer
1/2
Example 2: Complement
P(winning) = 0.35. Find P(not winning).
- 1P(not E) = 1 − P(E)
- 2= 1 − 0.35
Answer
0.65
Key Points to Remember
- ✓ 0 ≤ P(E) ≤ 1 for any event E
- ✓ Complementary events are mutually exclusive and exhaustive
- ✓ Equally likely assumption is essential for classical probability
Exam Tips
- • List sample space systematically for cards and dice
- • Use complement when 'at least one' is easier as 1 − P(none)
- • Simplify fractions in final answer
Practice MCQs — Probability
Test your understanding with topic-wise multiple choice questions. Explanations appear after each answer.
Question 1 of 6Score: 0/0
P(impossible event) equals: