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.

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P (mint and green) =

Answer 1

Use the inclusion–exclusion principle:
P(mint or green) = P(mint) + P(green) − P(mint and green).

So
0.35 = 0.30 + 0.20 − P(mint and green).

Therefore
P(mint and green) = 0.30 + 0.20 − 0.35 = 0.15.

P(mint and green) = 0.15 (15%).