Question

In a certain Algebra 2 class of 28 students, 11 of them play basketball and 13 of them play baseball. There are 11 students who play neither sport. What is the probability that a student chosen randomly from the class plays both basketball and baseball?

Answer 1

Probability of a student playing both basketball and baseball is 7/28

Explanation:

Step 1:

It is given the class has 28 students out of which 11 play basketball and 13 play baseball. It is also given that 11 students play neither sport.

Total number of students = 28

Students playing neither sport = 11

Students playing at least one sport = 28 - 11 = 17

Step 2:

Let N(Basketball) denote the number of students playing basketball and N(Baseball) denote the number of people playing baseball.

Then N(Basketball U Baseball) denotes the total number of students playing basketball and baseball and N(Basketball ∩ Baseball) denotes playing both basketball and baseball.

Since the number of students playing at least one sport is 17, N (Basketball U Baseball) = 17.

N (Basketball U Baseball) = N(Basketball) + N(Baseball) - N(Basketball ∩ Baseball)

N(Basketball ∩ Baseball) = N(Basketball) + N(Baseball) - N (Basketball U Baseball)

N(Basketball ∩ Baseball) = 11 + 13 - 17 = 7

Step 3:

Number of students playing both basketball and baseball = 7

Total number of students = 28

Probability of a student playing both basketball and baseball is 7/28

Step 4:

Answer:

Probability of a student playing both basketball and baseball is 7/28