Question

In a certain Algebra 2 class of 23 students, 11 of them play basketball and 13 of them play baseball. There are 8 students who play neither sport. What is the probability that a student chosen randomly from the class plays both basketball and baseball?

Answer 1

9/23

Explanation:

Of the 23 students, 9 play both baseball and basketball. The probability of choosing one of those is 9/23.

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Let A represent basketball, and B represent baseball. Then ...

P(A or B) = P(A) +P(B) -P(A and B)

Since 8 students play neither sport, we have ...

1 -8/23 = 11/23 +13/23 -P(A and B)

15/23 = 24/23 -P(A and B)

P(A and B) = (24 -15)/23

P(A and B) = 9/23