Question

in a recent semester at a local university 520 students enrolled in both general chemistry and calculus 1. Of these students 88 received an A in general chemistry 76 received an A in calculus, and 31 received an A in both general chemistry and calculus. Find the probability that a randomly chosen student received an A in general chemistry or calculus or both?

Answer 1

Let Ch and C denote the events of a student receiving an A in chemistry or calculus, respectively. We're given that

P(Ch) = 88/520

P(C) = 76/520

P(Ch and C) = 31/520

and we want to find P(Ch or C).

Using the inclusion/exclusion principle, we have

P(Ch or C) = P(Ch) + P(C) - P(Ch and C)

P(Ch or C) = 88/520 + 76/520 - 31/520

P(Ch or C) = 133/520