Question

In Exercises 16–18, use the following information. At a college, 43% of the students are women, 15% of the students are art majors, 4% have not chosen a major, and 8% are women and art majors. A faculty member conducts an experiment and selects students at random to participate.

16. What is the probability that a randomly selected student will be either a woman or an art major?
17. What is the probability that a randomly selected student is not a woman?
18. What is the probability that a randomly selected student is either an art
major or has not chosen a major?

Answer 1

This can be solved by sketching a Venn diagram.

Given:
a. 43% women
b. 8% women art majors
c. 15% art major
d. 4% not chosen major

16.
From (a) and (b),
15-8=7% are male art majors
So
P(art major∪woman)
=43%+7%=50%

17.
Assuming all students are either man or woman,
P(male)=100-43=57%

18.
Art major and those who have not chosen are mutually exclusive, so we add probabilities
P(art major ∪ not chosen)
=15+4
19%