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In a certain Algebra 2 class of 29 students, 13 of them play basketball and 14 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 29 students, 13 of them play basketball and 14 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?

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Solution

To solve this problem, we first need to find out how many students play either basketball or baseball.

We know that:

  • The total number of students is 29.
  • The number of students who play basketball is 13.
  • The number of students who play baseball is 14.
  • The number of students who play neither sport is 10.

So, the number of students who play either basketball or baseball is 29 (total students) - 10 (students who play neither) = 19 students.

Next, we need to find out how many students play both sports. We can do this by adding the number of basketball players and the number of baseball players, and then subtracting the number of students who play either sport.

So, the number of students who play both sports is 13 (basketball players) + 14 (baseball players) - 19 (students who play either sport) = 8 students.

Finally, we can find the probability that a student chosen randomly from the class plays both sports by dividing the number of students who play both sports by the total number of students.

So, the probability is 8 (students who play both sports) / 29 (total students) = 0.276 or 27.6% when expressed as a percentage.

This problem has been solved

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