Dependent Events
(KS3, Year 7)

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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. card_from_deck

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.

second card from deck

Picking cards without replacement are dependent events.

Lesson Slides

Picking coloured marbles from a bag, without replacing them, gives another example of dependent events. The slider below shows how the probabilities of picking a certain colored marble changes depending on whether that color has been picked before.

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.