Probability — Class 9 Maths (Samacheer Kalvi)
TN State Board (Samacheer Kalvi) Class 9 Mathematics, Chapter 9 (the final chapter). The mathematics of chance.
1. About this chapter
This chapter introduces the concept of probability, the types of events, and the measurement of probability for simple experiments.
2. Concept of probability
- A random experiment has more than one possible outcome (e.g., tossing a coin, rolling a die).
- Probability of an event A: P(A) = (number of favourable outcomes) / (total number of outcomes).
- Probability lies between 0 and 1: 0 ≤ P(A) ≤ 1.
3. Types of events
- Sure (certain) event: P = 1. Impossible event: P = 0.
- Complementary event: P(A′) = 1 − P(A) (A′ = "A does not happen").
- Equally likely outcomes have the same chance.
4. Worked examples
Example 1. A coin is tossed. Find P(getting a head). Favourable = 1, total = 2 → P = ½.
Example 2. A die is rolled. Find P(getting a number greater than 4). Favourable = {5, 6} = 2, total = 6 → P = 2/6 = ⅓.
Example 3. If P(A) = 0.7, find P(A′). P(A′) = 1 − 0.7 = 0.3.
5. Common mistakes
- Mistake: Writing a probability greater than 1. Fix: Always 0 ≤ P(A) ≤ 1.
- Mistake: Wrong total number of outcomes. Fix: Count all equally likely outcomes (e.g., a die has 6).
- Mistake: Forgetting the complement rule. Fix: P(A′) = 1 − P(A).
6. Practice (book-back style)
- Define probability of an event.
- A die is rolled. Find P(getting an odd number).
- A bag has 3 red and 2 blue balls. Find P(red).
- If P(A) = 0.25, find P(A′).
- What is the probability of an impossible event?
7. Answer key
- P(A) = favourable outcomes / total outcomes, with 0 ≤ P(A) ≤ 1.
- Odd = {1, 3, 5} = 3; P = 3/6 = ½.
- P(red) = 3/(3 + 2) = 3/5.
- P(A′) = 1 − 0.25 = 0.75.
- 0.
8. Quick revision
- Chapter 9 (final) · probability.
- P(A) = favourable / total; 0 ≤ P(A) ≤ 1.
- Sure event P = 1; impossible event P = 0.
- Complement: P(A′) = 1 − P(A).
- Count all equally likely outcomes correctly.
