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5/6 of the population of the country of Venezia lives in Mon

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emmak
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5/6 of the population of the country of Venezia lives in Mon [#permalink] 5/6 of the population of the country of Venezia lives in Mon   08 May 2013, 21:57
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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%
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Re: 5/6 of the population of the country of Venezia lives in Mon [#permalink] 5/6 of the population of the country of Venezia lives in Mon   08 May 2013, 22:24
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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%

Go thru the Attached Table

Regards,

Narenn
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Re: 5/6 of the population of the country of Venezia lives in Mon [#permalink] 5/6 of the population of the country of Venezia lives in Mon   08 May 2013, 23:38
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
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Re: 5/6 of the population of the country of Venezia lives in Mon [#permalink] 5/6 of the population of the country of Venezia lives in Mon   09 May 2013, 02:11
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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%

Total population = 60 (assume).

5/6*60=50 people from Montague.
1/5*60=10 people from Capulet.

0.2*50=10 people from Montague support Juliet.
0.7*10=7 people from Capulet support Juliet.

The probability that a Juliet supporter chosen at random resides in Capulet is 7/(10+7)=~41.

Answer: B.
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Re: 5/6 of the population of the country of Venezia lives in Mon [#permalink] 5/6 of the population of the country of Venezia lives in Mon   29 Apr 2015, 09:54
5/6 live in M so 1/6 live in C.

romeo in M = 5/6*4/5.
Julia in M = 5/6*1/5= 5/30 = 10/60
Julia in C = 1/6*7/10 =7/60.

Thus: 7/(7+10) = probability of a julia supporter coming from C. = 41%
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Re: 5/6 of the population of the country of Venezia lives in Mon [#permalink] 5/6 of the population of the country of Venezia lives in Mon   08 Jul 2021, 08:38
Juliets Supporters:
Montague: 0.2*(5/6)*x
Capulet: 0.7*(1/6)*x
So: Capulet + Montague = 100%

Choose a Capulet from Juliets Supporter:
CAPULET DIVIDE MONTAGUE + CAPULET

0.7*(1/6)*x DIVIDE 0.2*(5/6)*x + 0.7*(1/6)*x

From algebra you find that the total equal 7/17 = 0.41 aprox
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Re: 5/6 of the population of the country of Venezia lives in Mon [#permalink] 5/6 of the population of the country of Venezia lives in Mon   27 Jul 2024, 17:19
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Re: 5/6 of the population of the country of Venezia lives in Mon [#permalink]
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