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A jury pool consists of 6 men and w women. If 2 jurors

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Intern
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Joined: 09 Feb 2020
Posts: 3
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Re: A jury pool consists of 6 men and w women. If 2 jurors  [#permalink]

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New post 28 May 2020, 20:58
Bunuel
As per your solution, should we conclude that : if we should find the probability of x and y occurring at the same time (as per solution 1 man and 1 woman ) ,then if xy can also occur as yx -other things being equal- we should multiply by 2?
By that way the probability becomes almost double, kind of strange! Never seen that before.

Thank you in advance!
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A jury pool consists of 6 men and w women. If 2 jurors  [#permalink]

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New post 03 Jul 2020, 12:59
Bunuel wrote:
joshlevin90 wrote:
christianbze wrote:
I guess you did not understand the solution.

First, you have to find the probability for 2 men being picked and for 1 man and 1 woman being picked.

2 men:
- combinatorics: \(6 x 5\)
- all possibilities: \((6+w)(6+w-1)\)

1 man and 1 woman:
- combinatorics: \(6 x w x 2\)
- all possibilities: \((6+w)(6+w-1)\)
You can choose out of 6 men, w woman and you have two different places to set them.

So your inequality is:
\(\frac{6x5}{(6+w)(6+w-1)} > \frac{6 x w x 2}{(6+w)(6+w-1)}\)

\(\frac{30}{(6+w)(5+w)} > \frac{12 w}{(6+w)(5+w)}\)

as both denominators are the same, we just check the numerators.
So how long is \(30 > 12w\)?
As long as w (which has to be an integer!) is smaller than 3. So 0, 1, and 2.

So look at your options.


could you pls explain in detail how you got that equation?


A jury pool consists of 6 men and w women. If 2 jurors are selected from the pool at random, is the probability that 2 men will be selected higher than the probability that 1 man and 1 woman will be selected?

The total number of people in the jury = \(6+w\).
The probability of selecting 2 men when selecting 2 jurors = \(\frac{6}{6+w}*\frac{5}{(6+w)-1}=\frac{30}{(6+w)(5+w)}\);
The probability of selecting 1 man and 1 woman when selecting 2 jurors = \(2*\frac{6}{6+w}*\frac{w}{(6+w)-1}=\frac{12w}{(6+w)(5+w)}\): multiplying by 2 as MW can occur in two ways MW or WM;

The question asks: is \(\frac{30}{(6+w)(5+w)}>\frac{12w}{(6+w)(5+w)}\)? --> is \(30>12w\)? --> is \(w<2.5\)? So, the question basically asks whether there are 2, 1, or 0 women in the jury.


(1) w ≥ 3. Directly gives a NO answer to the question. Sufficient.

(2) w < 6. Not sufficient.

Answer: A.

Similar questions to practice:
http://gmatclub.com/forum/a-jar-contain ... 01748.html (almost the same question from MGMAT)
http://gmatclub.com/forum/a-certain-jar ... 04924.html
http://gmatclub.com/forum/if-2-differen ... 28233.html
http://gmatclub.com/forum/a-certain-box ... 53384.html

Hope this helps.


Bunuel GMATNinja

Why do we not multiply when we use 6C1*wC1, but we do when using probability formulae?
GMAT Club Bot
A jury pool consists of 6 men and w women. If 2 jurors   [#permalink] 03 Jul 2020, 12:59

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