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

Question

Mathematics

Alonzo Cantu

17 December, 04:23

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

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Answers (1)

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Colt Beard · Answer 1

0.25

Step-by-step explanation:

40% of the students use mac computer

67% of the students are undergraduate

23% of the students are graduates and use mainly PC

Students that use PC computers = 100 - 40 = 60%

Students that are graduates = 100 - 67 = 33%

Students that are graduates that use Mac = 33 - 23 = 10%

Students that are undergraduate that use PC = 67 - 30 = 37%

Using conditional probability

Pr (B|A) = Pr (A and B) / Pr (A)

Pr (Graduate | mac) = Pr (graduate and mac) / Pr (mac)

= 10% / 40%

= 1/4

= 0.25