# Independent events

Events where one result has no effect on the other. To find the chance of both happening, multiply their probabilities.

Maths (school) · Part 08: Probability and statistics · Card 4 of 8 · Last updated 2026-10-19

## Analogy

Like flipping two separate coins: the first coin cannot influence the second.

## Example

**Roll a dice twice**

P(6 then 6) = 1/6 x 1/6
= 1/36
Two heads: 1/2 x 1/2 = 1/4

## In practice

Winning the lottery twice in a row uses independent events.

## Practice

### Flashcards

- **What is the probability of two heads with two fair coins?** 1/4 (1/2 x 1/2).

### Interview questions

**A bag has 3 red and 2 blue counters. Two are taken without replacement. Find the probability both are red and explain.**

- First red: 3/5
- Second red: 2/4 as one red is gone
- Multiply along the branch
- 3/5 x 2/4 = 6/20 = 3/10

## Questions people ask

### Why do you multiply for independent events?

You want the chance of the first thing and then the second. Each probability is a fraction of the one before. A half of a half is a quarter. So two heads in a row has probability 1/2 x 1/2 = 1/4.

### What does 'and' mean in probability questions?

'And' means both events must happen, so you multiply. 'Or' means either can happen, so you add (if they cannot overlap). Spotting these two key words helps you pick the right operation. For example, the chance of heads and then a 6 on a dice is 1/2 x 1/6 = 1/12.

## Related concepts

- [Tree diagrams](https://studyvisually.com/learn/science/maths-school/maths-school-part-8/maths-school-part-8-concept-5)
- [Probability scale](https://studyvisually.com/learn/science/maths-school/maths-school-part-8/maths-school-part-8-concept-1)
- [Relative frequency](https://studyvisually.com/learn/science/maths-school/maths-school-part-8/maths-school-part-8-concept-2)
- [Mutually exclusive events](https://studyvisually.com/learn/science/maths-school/maths-school-part-8/maths-school-part-8-concept-3)

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