---
source: ncert
topic: probability
class_level: class_9
chapter: ch15
difficulty: intermediate
---

Class 9 | Ch15: Probability
BASIC CONCEPTS:
Experiment: activity with defined set of outcomes. e.g., throwing die, tossing coin.
Sample space: set of ALL possible outcomes. S={H,T} for coin. S={1,2,3,4,5,6} for die.
Event: subset of sample space. Any collection of outcomes.
PROBABILITY FORMULA:
P(E) = Number of favourable outcomes / Total number of outcomes.
Range: 0 <= P(E) <= 1.
P(certain event) = 1. P(impossible event) = 0.
COMPLEMENTARY EVENT:
P(E) + P(not E) = 1. So P(not E) = 1 - P(E).
TYPES OF EVENTS:
Simple event: single outcome. Compound event: more than one outcome.
Mutually exclusive: cannot occur simultaneously. P(A or B)=P(A)+P(B).
EQUALLY LIKELY OUTCOMES: each outcome has same probability of occurring.
STANDARD PROBLEMS:
Die: P(even)=3/6=1/2. P(prime)=3/6=1/2 (2,3,5). P(>4)=2/6=1/3 (5,6).
Coin: P(H)=1/2. Two coins: P(both H)=1/4. P(at least one H)=3/4.
Cards (52): P(ace)=4/52=1/13. P(face card)=12/52=3/13. P(red)=26/52=1/2.
Two dice: Total outcomes=36. P(sum=7): (1,6),(2,5),(3,4),(4,3),(5,2),(6,1)=6/36=1/6.
SOLVED EXAMPLES:
Example 1: Bag has 5 red, 7 blue, 3 green balls. Total=15.
P(red)=5/15=1/3. P(not blue)=(15-7)/15=8/15. P(green or red)=8/15.
Example 2: Two dice thrown. P(sum=8)?
Pairs: (2,6),(3,5),(4,4),(5,3),(6,2)=5 pairs. P=5/36.
Example 3: Cards. P(king or queen)?
Kings=4, Queens=4. Total face cards include these. P(king or queen)=8/52=2/13.
COMMON MISTAKES:
P(E) must be between 0 and 1 inclusive.
For two dice: total outcomes=36 (not 12). Each die independent.
P(not E)=1-P(E), NOT P(E)-1.