Independent and Dependent Events
# Independent and Dependent Events

GCSE(F) GCSE(H)

Two events are **independent** when the result of one event does not affect the result of the other event.

An event becomes **dependent** when the result of a an earlier events affects the result of the subsequent event.

Typically, events become dependent when the total number of possibilities change between events.

## Examples

1. A bag contains 5 red balls and 3 green balls. A red ball is drawn and replaced. What is the probability of selecting a red ball on a second draw?

Answer: `frac(5)(8)`

The events are independent. The probability of selecting a red ball on the second draw is 5 out of 8, or `frac(5)(8)`

2. A bag contains 5 red balls and 3 green balls. A red ball is drawn and is not replaced. What is the probability of selecting a red ball on a second draw?

Answer: `frac(4)(7)`

The events are dependent, as there are now only 4 red balls in the bag, and a total of 7 balls altogether. The probability of drawing a second red ball is now 4 out of 7, or `frac(4)(7)`.

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