A Universiy took a poll of its graduating students 30 of stu

A Universiy took a poll of its graduating students. 30% of students said they took a humanities course, 48% of students said they took a economics course and 20% said they took both a humanities and an economics course.

(a) What is the probability that a randomly selected graduating student took a humanities or an economics course?

(b) What is the probability that a randomly selected graduating student took a humanities but not an economics course?

(c) What is the probabiity that a randomly selected graduating student did not take a humanities nor an economics course?

(d) What is the probability that a randomly selected graduating student took exactly one of these types of courses?

Solution

a) the probability that a randomly selected graduating student took a humanities or an economics course

= P(AUB)

= 0.30+0.48-0.20 = 0.58

b) the probability that a randomly selected graduating student took a humanities but not an economics course

= P(A-B)

= P(A)-P(AB)

=0.30-0.20

=0.10

c) the probabiity that a randomly selected graduating student did not take a humanities nor an economics course

= P(A\'B\')

= 1-{P(AUB)}

= 0.42

d) the probability that a randomly selected graduating student took exactly one of these types of courses

= P(A-B)+P(B-A)

= 0.38