Class 9 Maths Chapter 15 Probability NCERT Solutions | Complete Guide with Examples

Class 9 Maths Chapter 15 – Probability

Introduction

Probability is about chance. It tells us how likely an event is to happen.

For example:

• What is the chance of getting a head when tossing a coin?

• What is the chance of getting a number greater than 4 on a dice?

This chapter helps you understand these situations using simple formulas.

Basic Terms

Experiment: An action like tossing a coin or rolling a dice
Outcome: Result of an experiment
Event: A set of outcomes
Sample Space (S): All possible outcomes

Formula Used

Probability Formula

P(E) = Number of favourable outcomes / Total number of outcomes

P(E) = n(E) / n(S)

Important Points

• 0 ≤ P(E) ≤ 1

• P(E) = 0 → Impossible event

• P(E) = 1 → Certain event

Exercise 15.1 Solutions

Question 1

A coin is tossed once. Find probability of getting a head.

Solution:
Sample space S = {H, T}
Total outcomes = 2

Favourable outcome = {H} → 1

P(H) = 1 / 2

Question 2

A dice is thrown once. Find probability of getting number 4.

Solution:
S = {1,2,3,4,5,6}
Total outcomes = 6

Favourable = {4} → 1

P(4) = 1 / 6

Question 3

Find probability of getting a number greater than 4.

Solution:
Favourable outcomes = {5,6} → 2

P = 2 / 6 = 1 / 3
Question 4

Find probability of getting a number less than 3.

Solution:
Favourable outcomes = {1,2} → 2

P = 2 / 6 = 1 / 3

Question 5

A card is drawn from a deck. Find probability of getting a red card.

Solution:
Total cards = 52
Red cards = 26

P = 26 / 52 = 1 / 2

Question 6

Find probability of getting a king.

Solution:
Kings = 4

P = 4 / 52 = 1 / 13

Question 7

Find probability of getting a non-face card.

Solution:
Face cards = 12

Non-face cards = 52 − 12 = 40

P = 40 / 52 = 10 / 13

Question 8

A number from 1 to 10 is selected. Find probability of getting even number.

Solution:
Even numbers = {2,4,6,8,10} → 5

Total = 10

P = 5 / 10 = 1 / 2

Question 9

Find probability of selecting a vowel from letters of "MATHEMATICS".

Solution:
Letters = 11

Vowels = A, E, A, I → 4

P = 4 / 11

Question 10

Find probability of getting tail when coin is tossed.

Solution:
P(T) = 1 / 2

Important Tips

• Always write sample space clearly

• Count outcomes carefully

• Simplify fractions

• Read question properly before solving