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.

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?

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

Answer: `frac(5)(8)`

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?

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)`.

If a green ball had been drawn first, then the probability of drawing a red ball as the second ball would be different.

Answer: `frac(4)(7)`

Check out our iOS app: tons of questions to help you practice for your GCSE maths. Download free on the App Store (in-app purchases required).