## The Lesson

An event is independent if its outcome does not affect the probability of other events occuring.## Real Examples of Independent Events

It is easier to understand independent events with examples.## Tossing a Coin

If a coin is tossed, the probability of it landing**Heads**is

**.**

^{1}⁄_{2}If a coin is tossed a 2

^{nd}time, the probability of it landing

**Heads**is still

**.**

^{1}⁄_{2}Each toss does not affect the probability of another toss. Coin tosses are independent events.

## Rolling a Die

If a die is rolled, the probability of getting a**2**is

**.**

^{1}⁄_{6}If a die is rolled a 2

^{nd}time, the probability of getting a

**2**is still

**.**

^{1}⁄_{6}Each die roll does not affect the probability of another roll. Die rolls are independent events.

## Top Tip

## An Event Is Not Independent If the Probability Changes When It Is Repeated

Probability depends on the number of ways an outcome can occur and how many outcomes there are for an event. For example, when tossing a coin, there is always**1**way a

**Heads**can come up and

**2**outcomes (

**Heads**and

**Tails**). These don't change no matter how many times a coin is tossed. Now consider picking the

**Ace of Spades**from a pack of cards, without replacing it. In the 1

^{st}pick, there are

**52**possible outcomes (one for each card). In the 2

^{nd}pick, one card has been removed... ...so the number of possible outcomes has changed... ...so the probability has changed... ...so the event is not independent.