Chapter 5.3, Problem 70E

To determine

Probability for randomly selected person is a graduate student.

Answer to Problem 70E

Probability that the randomly selected person is graduate student is approx. 0.5625.

Explanation of Solution

Given information:

60% of the students mainly use MACs.

67% are undergraduates.

23% are graduates who mainly use a MAC.

Let

G: for graduates

U: for undergraduates

MAC: for MAC users

Corresponding probabilities are:

Probability for MAC users,

  $P\left(\text{MAC}\right)=0.60$

Probability for undergraduates,

  $P\left(\text{U}\right)=0.67$

Probability for graduate and MAC users,

  $P\left(\text{G}\text{and}\text{MAC}\right)=0.23$

Since the randomly selected person mainly uses a MAC.

Apply the conditional probability:

  $P\left(\text{G}|\text{MAC}\right)=\frac{P\left(\text{G}\text{and}\text{MAC}\right)}{P\left(\text{MAC}\right)}=\frac{0.23}{0.60}=\frac{23}{60}\approx 0.3833$

Thus,

Probability that the randomly selected person is a graduate student is approx. 0.3833.