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Chapter 5: Q. 70. (page 330)

Mac or PC? A recent census at a major university revealed that 60% of its students mainly used Macs. The rest mainly used PCs. At the time of the census, 67% of the school’s students were undergraduates. The rest were graduate students. In the census, 23% of respondents were graduate students and used a Mac as their main computer. Suppose we select a student at random from among those who were part of the census and learn that the person mainly uses a Mac. Find the probability that the person is a graduate student.

Short Answer

Expert verified

The probability that the randomly selected person is a graduate student is approx0.3833.

Step by step solution

01

Given information

60%of the students mainly use MACs.

67%are undergraduates.

23%are graduates who mainly use a MAC.

02

Explanation

G: for graduates

U: for undergraduates

MAC: for MAC users

The probabilities are as follows:

Probability for MAC users,

P(MAC)=0.60

Undergraduates' probability,

P(U)=0.67

Graduates and MAC users have a higher chance of succeeding.

P(GandMAC)=0.23

Because the person who was chosen at random primarily uses a Mac.

Use the conditional probability formula:

P(G∣MAC)=P(Gand MAC)P(MAC)=0.230.60=2360≈0.3833

Therefore, the probability that the randomly selected person is a graduate student is approx0.3833.

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