Independent and Dependent Events

## Independent and Dependent Events

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.

## Example 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?

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)

## Example 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?

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)