Question

A dish contains hard candies of various flavors and various colors.

​

​Of the ​candies in the dish,
30
%
30% are mint and
20
%
20% are green.

​

​A piece of candy is to ​be selected at random from the dish.

​

​The probability that the selected piece ​of candy will be mint or green is
0.35
0.35.

​

​What is the probability that the ​selected piece of candy will be both mint and green?

​

​Show your work on the scratchpad.

Answer 1

Let M = event "mint", G = event "green". Use the inclusion–exclusion formula:

P(M ∪ G) = P(M) + P(G) − P(M ∩ G).

Plug in values: 0.35 = 0.30 + 0.20 − P(M ∩ G).

So P(M ∩ G) = 0.30 + 0.20 − 0.35 = 0.15.

Answer: 0.15 (15%).