| --- |
| 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. |
