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A business school club, Friends of Foam, is throwing a party

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Joined: 25 Aug 2004
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A business school club, Friends of Foam, is throwing a party [#permalink] New post 26 Dec 2004, 11:37
A business school club, Friends of Foam, is throwing a party at a local bar. Of the business school students at the bar, 40% are first year students and 60% are second year students. Of the first year students, 40% are drinking beer, 40% are drinking mixed drinks, and 20% are drinking both. Of the second year students, 30% are drinking beer, 30% are drinking mixed drinks, and 20% are drinking both. A business school student is chosen at random. If the student is drinking beer, what is the probability that he or she is also drinking mixed drinks?

A. 2/5
B. 4/7
C. 10/17
D. 7/24
E. 7/10
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 [#permalink] New post 26 Dec 2004, 15:42
C: 10/17

Its conditional probability.
Let x be the number of people at the party.. FY students = 0.4x and Second year = 0.6x.

P(drinking mixed given drinking beer) = p (drinking both mixed and beer) /
P(drinking beer).

= (0.4*0.2 + 0.6*0.2)x / (0.4*0.4 + 0.6*0.3)x = 0.2/0.34 = 10/17.
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 [#permalink] New post 26 Dec 2004, 20:16
If there are 100 students total then Total sample space of beer drinking students = 34. Total for students drinking both is 20.

P(E) = P(E) / P(S) = 20/34 = 10/17
  [#permalink] 26 Dec 2004, 20:16
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A business school club, Friends of Foam, is throwing a party

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