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08 May 2013, 21:57
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
69% (02:52) correct
31%
(02:55)
wrong
based on 570
sessions
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5/6 of the population of the country of Venezia lives in Montague Province, while the rest lives in Capulet Province. In the upcoming election, 80% of Montague residents support Romeo, while 70% of Capulet residents support Juliet; each resident of Venezia supports exactly one of these two candidates. Rounded if necessary to the nearest percent, the probability that a Juliet supporter chosen at random resides in Capulet is
(A) 28%
(B) 41%
(C) 45%
(D) 72%
(E) 78%
(A) 28%
(B) 41%
(C) 45%
(D) 72%
(E) 78%
08 May 2013, 22:24
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emmak
5/6 of the population of the country of Venezia lives in Montague Province, while the rest lives in Capulet Province. In the upcoming election, 80% of Montague residents support Romeo, while 70% of Capulet residents support Juliet; each resident of Venezia supports exactly one of these two candidates. Rounded if necessary to the nearest percent, the probability that a Juliet supporter chosen at random resides in Capulet is
(A) 28%
(B) 41%
(C) 45%
(D) 72%
(E) 78%
(A) 28%
(B) 41%
(C) 45%
(D) 72%
(E) 78%
Go thru the Attached Table
Regards,
Narenn
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General Discussion
08 May 2013, 23:38
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ratio of residents is 5:1 (montague : capulet).
In montague, 20% vote for Juliette. In capulet, 70% vote for Juliette.
Since population ratio is 5:1, there are five voters in montague for every voter in capulet.
20% of 5 is 1, which represents the Juliette voters in Montague
70% of 1 is .7, which represents the Juliette voters in Capulet
Now we need to find out what percentage that .7 is of the total... so we take \(\frac{.7}{(1 + .7)}\)
\(= \frac{7}{17}\)
I'm not a big fan of long division, but we need to get this number into percentage form.
\(\frac{(7*6)}{(17*6)} = \frac{42}{102}\) which is pretty darn close to 41, so the answer is B
In montague, 20% vote for Juliette. In capulet, 70% vote for Juliette.
Since population ratio is 5:1, there are five voters in montague for every voter in capulet.
20% of 5 is 1, which represents the Juliette voters in Montague
70% of 1 is .7, which represents the Juliette voters in Capulet
Now we need to find out what percentage that .7 is of the total... so we take \(\frac{.7}{(1 + .7)}\)
\(= \frac{7}{17}\)
I'm not a big fan of long division, but we need to get this number into percentage form.
\(\frac{(7*6)}{(17*6)} = \frac{42}{102}\) which is pretty darn close to 41, so the answer is B
