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Chapter 5: Q 96. (page 331)

Mac or PC? A recent census at a major university revealed that 40% of its students mainly used Macintosh computers (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 the respondents were graduate students who said that they used PCs as their

primary computers. Suppose we select a student at random from among those who were part of the census and learn that the student mainly uses a Mac.

Find the probability that this person is a graduate student. Show your work.

Short Answer

Expert verified

The probability that the person is a graduate student is 0.25

Step by step solution

01

Step 1. Given Information

A MAC is used by 40% of people. Undergraduates make up 67%of the group. Only 23% of grads use a computer exclusively.

02

Step 2. Concept used

Conditional probability: P(B|A)=P(AandB)/P(A)

03

Step 3. Calculation

Combining the above data to get the following two-way table, according to the question

Conditional probability: P(B|A)=P(AandB)/P(A)

Assess using the two-way table, as follows:

PGraduate/MAC)=P(GraduateandMAC)/P(MAC)

=10%40%=14=0.25

As a result, there is a 0.25chance that the person is a graduate student.

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