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# math question

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Intern
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math question [#permalink]  04 Feb 2004, 05:01
Question from Deltacourse

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
Intern
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[#permalink]  04 Feb 2004, 06:50
C??
SVP
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[#permalink]  04 Feb 2004, 07:55
i dont get any of the answers you have mentioned. Let us say 100 students
F = 40
FB = 16 First year drinking beer (40%)
FM = 16 First year drinking mixed drinks (40%)
FBoth = 8 First year drinking both (20%)

S = 60
SB = 18 Second year drinking beer (30%)
SM = 18 Second year drinking mixed drinks (30%)
SBoth = 12 Second year drinking both (20%)

P = Drinking Both / Total
= (8+12)/100 = 1/5

or could it be
( 8+12) / ( 16+18 ) = 20/34 or 10/17
Manager
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[#permalink]  04 Feb 2004, 09:23
B...drinks beer
M...drinks mixed drinks
BM...drinks both
┬з...drinks none
1...first year student
2...second year student

1: Total 40% of the population
B: 16% of the total
M: 16%
BM: 8%
┬з: 0%

2: Total 60%
B: 18%
M: 18%
BM: 12%
┬з: 12%

Overall:
B: 34%
M: 34%
BM: 20%
┬з: 12%

Following is the formula - conditional prob
P(M/B) = P(M intersection B) / P(B)

P(M/B) means given that B has occured what is the probability that M also occurs.

Therefore,
P(M/B) = (8+12) / (16 +18)
= 10/17

Hope this helps
Intern
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[#permalink]  04 Feb 2004, 10:50

But my solution was little bit other. I have taken as number of possible
outcomes 54 ( 18+16 and 8+12) and got 10/27.
Could someone explain pls why we should take 34?
I think that if student chosen drinks a beer it is possible that he beongs either to only beer drinkers or mixed drinkers which number is 54.
Intern
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[#permalink]  04 Feb 2004, 11:24
ALik, the chosen student is definitely drinking beer, so the sample space will be the sum of beer drinkers only. Hence 34!!
[#permalink] 04 Feb 2004, 11:24
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