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

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

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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.

Manager
Joined: 02 Dec 2018
Posts: 62
A jury pool consists of 6 men and w women. If 2 jurors  [#permalink]

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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.

$$\frac{6x5}{(6+w)(6+w-1)} > \frac{6 x w x 2}{(6+w)(6+w-1)}$$

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

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.

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.

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?
A jury pool consists of 6 men and w women. If 2 jurors   [#permalink] 03 Jul 2020, 12:59

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