In a certain Algebra 2 class of 27 students, 5 of them play basketball and 15 of them play baseball. There are 10 students who play neither sport. What is the probability that a student chosen randomly from the class plays both basketball and baseball?
Question
In a certain Algebra 2 class of 27 students, 5 of them play basketball and 15 of them play baseball. There are 10 students who play neither sport. What is the probability that a student chosen randomly from the class plays both basketball and baseball?
Solution
To solve this problem, we first need to find out how many students play both basketball and baseball.
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We know that 5 students play basketball and 15 students play baseball. But this total (5+15=20) includes students who play both sports.
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We also know that 10 students play neither sport. So, the total number of students who play at least one sport is 27 (total students) - 10 (those who play neither) = 17 students.
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Therefore, the number of students who play both sports is 20 (those who play basketball or baseball) - 17 (those who play at least one sport) = 3 students.
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The probability that a student chosen randomly from the class plays both sports is therefore 3 (students who play both) / 27 (total students) = 1/9.
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