S†atistics: Proportion

Question

At Cityville High School, 36% of the students participate in sports, 36% of the students participate in academic clubs, and 13% of the students participate in both sports and academic clubs.

Find the proportion of students who participate in either sports or academic clubs.

Answer 1

Use the definition of the probability of a union of events. For any given distribution and events A and B, we have

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

In your case, events A and B correspond to A = {students participate in sports} and B = {students participate in academic clubs} so that,

P(A ∪ B) = 0.36 + 0.0.36 - 0.13 = 0.59