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# probability

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In a certain Algebra 2 class of 26 students, 18 of them play basketball and 7 of them play baseball. There are 5 students who play neither sport. What is the probability that a student chosen randomly from the class plays both basketball and baseball?

Mar 22, 2023

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We can use the principle of inclusion-exclusion to find the number of students who play both basketball and baseball. The total number of students who play at least one sport is the sum of those who play basketball and those who play baseball, minus the number who play both sports, since they were counted twice.

So we have:

Total = Basketball + Baseball - Both + Neither 26 = 18 + 7 - Both + 5

Simplifying this equation, we get:

Both = 4

Therefore, there are 4 students who play both basketball and baseball.

The probability of choosing one of these students randomly from the class is:

P(both) = number of students who play both sports / total number of students P(both) = 4 / 26 P(both) = 0.1538 (rounded to four decimal places)

So the probability that a student chosen randomly from the class plays both basketball and baseball is approximately 15.38%

Mar 22, 2023