Question

In a certain Algebra 2 class of 27 students, 11 of them play basketball and 9 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

Answer:

The probability of students who play both basketball and baseball =  $\frac{4}{27}$

Step-by-step explanation:

In a certain Algebra class,

The total number of students = 27 students

Let the students playing basketball be represented as A and baseball as B.

The students who play basketball, A= 11

The students who play basetball,B =9

The students who play neither sport,  = 11

The students who play both basketball and baseball,  = ?

By formula, P(AUB)=P(A)+P(B)-P(A∩B)

Substituting the values in the equation, we get

P(AUB) = $\frac{11}{27} + \frac{9}{27} - \frac{16}{27}$

 P(AUB) = $\frac{4}{27}$

The probability of students who play both basketball and baseball =  $\frac{4}{27}$