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# Dependent Events

(KS3, Year 7)

## The Lesson

An event is dependent if its probability is affected by whether or not another event has occured.## A Real Example of a Dependent Event

It is easier to understand a dependent event with an example.## Picking Cards

If a card is picked from a pack,**1**card is picked from a deck of

**52**cards. The probability is

**.**

^{1}⁄_{52}If the card that has been picked is not put back into the deck, there will be 1 less card in the deck. If a 2

^{nd}card is picked from the deck,

**1**card is picked from a deck of

**51**cards. The probability is

**.**

^{1}⁄_{51}Picking cards without replacement are dependent events.

## Top Tip

## An Event Is Dependent 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 dependent.

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