Answer to Question #242744 in Statistics and Probability for CLYDE63

Question

In a certain Algebra 2 class of 30 students, 7 of them play basketball and 11 of them play baseball. There are 5 students who play both sport. What is the probability that a student chosen randomly from the class plays basketball or baseball?

Answer 1

Let A denote the event that a student plays basketball and B the event that a student plays baseball.

p(A)=7/30

p(B)=11/30

The event that a student plays both basketball and baseball is the intersection of event A and B. It is given by, (A AND B).The probability for this event is,

p(A AND B)=5/30

Probability that a student chosen randomly from the class plays basketball or baseball is,

p(A OR B).

p(A OR B) is obtained using addition property of probability given as,

p(A OR B)=p(A)+p(B)-p(A AND B)

=7/30+11/30-5/30

=18/30-5/30

=13/30