Question

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

The probability that the person is a graduate student is $0.25$

Step-by-step solution

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.

Step 2. Concept used

Conditional probability: $P\left(B\right|A)=P(AandB)/P(A)$

Step 3. Calculation

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

Conditional probability: $P\left(B\right|A)=P(AandB)/P(A)$

Assess using the two-way table, as follows:

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

$=\frac{10\%}{40\%}=\frac{1}{4}=0.25$

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