EXAMPLE 3.5.19

In his pocket, Gomer has 3 red, 5 orange and 2 blue M-and-Ms. If he randomly chooses two M&Ms, what is the probability that both will be red?

D. .52

SOLUTION

Let E be the event that the first M-and-M is red. Let F be the event that the second M-and-M is red. Since we are choosing two items from a small population of specified size, we will treat these events as DEPENDENT (that is, the probability of the second event is significantly affected by the occurrence of the first event).

The probability that the first M-and-M is red is 3/10 (there are 10 M-and-Ms, 3 of which are red).

Assuming that the first M-and-M is red, the probability that the second one will be red is 2/9 (there are 9 M-and-Ms remaining, 2 of which are red). Thus,