Question

In a certain Algebra 2 class of 28 students, 17 of them play basketball and 9 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?

Answer 1

Probability of a student playing both basketball and baseball is 3/28

Step-by-step explanation:

Step 1:

It is given the class has 28 students out of which 17 play basketball and 9 play baseball. It is also given that 5 students play neither sport.

Total number of students = 28

Students playing neither sport = 5

Students playing atleast one sport = 28 - 5 = 23

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 atleast one sport is 23, N (Basketball U Baseball) = 23.

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) = 17 + 9 - 23 = 3

Step 3:

Number of students playing both basketball and baseball = 3

Total number of students = 28

Probability of a student playing both basketball and baseball is 3/28

Step 4:

Answer:

Probability of a student playing both basketball and baseball is 3/28