## 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 12. If a coin is tossed a 2nd time, the probability of it landing Heads is still 12. 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 16. If a die is rolled a 2nd time, the probability of getting a 2 is still 16. Each die roll does not affect the probability of another roll. Die rolls are independent events.

## 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 1st pick, there are 52 possible outcomes (one for each card). In the 2nd 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.