Probability: Class 9 Study Guide
Probability measures how likely something is, as a number from 0 (impossible) to 1 (certain).
An experiment is an action with results we can observe, such as tossing a coin or rolling a die. Each result is an outcome, and a group of outcomes is an event.
In Class 9 the empirical probability of an event is found from trials: probability = number of trials in which the event happens ÷ total number of trials.
Finding probability from results
A coin is tossed 100 times and heads appears 46 times. The empirical probability of heads is 46 ÷ 100 = 0.46. As the number of tosses grows, the result usually moves closer to 0.5.
The total number of times the experiment was done.
How often the event happened.
Successes ÷ trials.
The answer must be between 0 and 1.
Useful facts
The probability of an impossible event is 0, for example getting a 7 on an ordinary die. The probability of a certain event is 1, for example getting a number from 1 to 6. The probabilities of all the outcomes of an experiment add up to 1. The probability of an event not happening is 1 minus the probability of it happening.
| Event (one die roll) | Probability |
|---|---|
| Getting a 4 | 1/6 |
| Getting an even number | 3/6 = 1/2 |
| Getting a number greater than 6 | 0 |
| Getting a number less than 7 | 1 |
Worked examples and common mistakes
Example: In a class of 40 students, 14 walk to school. The probability that a student chosen at random walks is 14 ÷ 40 = 0.35. Example: The probability of rain is 0.3, so the probability of no rain is 1 − 0.3 = 0.7. Common mistakes: giving a probability larger than 1, and thinking a coin that gave 3 heads in a row is now more likely to give tails.
Check your understanding: model answers
1. 1. 2. 9 ÷ 60 = 0.15. 3. No, it must lie between 0 and 1.
✨ Key Takeaways
- Probability is a number from 0 to 1.
- Empirical probability comes from trials.
- The probabilities of all outcomes add to 1.
- P(not A) = 1 − P(A).
💬 Questions for Discussion & Reflection
- What is the probability of a certain event?
- A die is rolled 60 times and 9 gives a six. What is the empirical probability of a six?
- Can a probability be 1.5?