Question

In a certain Algebra 2 class of 21 students, 10 of them play basketball and 9 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

Explanation:

out of the 21 students, 8 do not play neither basketball nor baseball.

so, 13 students play at least one of these games.

10 play basketball, and 9 play baseball. that would be 19 together. but we have only 13 players.

that means 6 students (19 - 13) must play both games.

remember, a probability is always

desired cases / possible cases

so, when we are looking for the students, who play both games, we have 6 desired cases out of a total of 21.

and the probability to pick one of them is therefore

6/21 = 2/7 = 0.285714286...