# Probability · Year 9

> Probability, Year 9: The probability of a simple event and more. Explanation, worked examples and free practice for the national curriculum in England.

In Probability (Year 9) you practise 4 skills: The probability of a simple event · Probability and relative frequency · The complementary event · Which is more likely? Comparing probabilities.

A probability is a number from 0 to 1 that says how likely an event is to happen. An impossible event has a probability of 0, and a certain event a probability of 1.

When all the outcomes are equally likely, the probability is the number of wanted outcomes divided by the number of all the outcomes.

When an experiment is repeated many times, the relative frequency of an outcome gets close to its probability.

The complementary event is ‘the event does not happen’. The probabilities of an event and of its complement add up to 1.

**Tip:** Before you work anything out, count all the possible outcomes, and then the wanted ones.

## What you learn

### The probability of a simple event

- Example: A bag contains 2 red balls and 9 blue balls. One ball is taken out without looking. What is the probability of taking out a red ball?
- Answer: 2/11
- Solution: There are 11 balls in the bag, and 2 of them are red. The probability is: 2/11

### Probability and relative frequency

- Example: A class took a ball out of a bag 10 times, putting it back each time, and a red ball came out 5 times. What is the estimated probability of getting a red ball? Give your answer as a fraction.
- Answer: 1/2
- Solution: The estimated probability is 5/10 .

### The complementary event

- Example: The probability that it will rain tomorrow is 3/4 . What is the probability that it will not rain tomorrow?
- Answer: 1/4
- Solution: 1 − 3/4 = 4/4 − 3/4 = 1/4

### Which is more likely? Comparing probabilities

- Example: A bag contains 2 red balls, 8 blue balls and 2 green balls. One ball is taken out without looking. Which is more likely: taking out a red ball or taking out a green ball?
- Options: The same chance · A green ball · A red ball
- Answer: The same chance
- Solution: The probabilities are 2/12 and 2/12 . They are equal: both colours have the same chance.

The exercises are made by rules and the answers are worked out in code. The topic follows the national curriculum in England: mathematics (key stages 3 and 4).

[Practise on the site](https://kixplo.com/uk/en/) · [All Year 9 topics](https://kixplo.com/uk/en/maths/year-9/)