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

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by BTGmoderatorAT » Sat Mar 10, 2018 6:54 am
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?

(1) w ≥ 3
(2) w < 6

What's the best way to determine whether statement 1 is sufficient? Need any experts help please?
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by mbawisdom » Sat Mar 10, 2018 7:54 am
ardz24 wrote: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?

(1) w ≥ 3
(2) w < 6

What's the best way to determine whether statement 1 is sufficient? Need any experts help please?
Hi ardz24! Great question, happy to help out. Interesting that you ask about the first statement but not the second. How did you solve the second part? Once you set up your equation for the probabilities you should take the same approach for each statement so am a bit confused as to how you can do 2 but not do 1. Let me know where you got to and if you still need help will be happy to show you how I would answer the question.
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by GMATGuruNY » Sat Mar 10, 2018 10:05 am
ardz24 wrote: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?

(1) w ≥ 3
(2) w < 6
Statement 1:
Case 1: w=3, for a total of 9 people (6 men and 3 women)
From the 6 men, the number of ways to choose 2 = 6C2 = (6*5)/(2*1) = 15.
From the 9 people, the number of ways to choose 1 man and 1 woman = (number of options for the 1 man)(number of options for the 1 woman) = 6*3 = 18.
Since the value in blue is GREATER than the value in red, P(1 man and 1 woman) > P(2 men), with the result that the answer to the question stem is NO.

If the number of women increases, then the value in blue will also increase, while the value in red will stay the same.
Thus -- in every case -- P(1 man and 1 woman) > P(2 men), with the result that the answer to the question stem is NO.
SUFFICIENT.

Statement 2:
Case 1 also satisfies Statement 2.
In Case 1, the answer to the question stem is NO.
Case 2: w=0
In this case, the jury pool is all MEN, so P(2 men) = 100% and P(1 man and 1 woman) = 0%.
Thus, the answer to the question stem is YES.
Since the answer is NO in Case 1 but YES in Case 2, INSUFFICIENT.

The correct answer is A.
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by Brent@GMATPrepNow » Mon Mar 12, 2018 7:25 am
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?

(1) w> 3

(2) w < 6
Target question: Is P(2 men) greater than P(1 man and 1 woman)?

Statement 1: w> 3
Let's see what happens if w = 3 (note: this is the best chance that P(2 men) will be greater than P(1 man and 1 woman)

P(2 men) = P(man selected 1st and man selected 2nd)
= (6/9)(5/8)
= 30/72

P(1 man and 1 woman) = P(man selected 1st and woman selected 2nd OR woman selected 1st and man selected 2nd)
= P(man selected 1st and woman selected 2nd) + P(woman selected 1st and man selected 2nd)
= (6/9)(3/8) + (3/9)(6/8)
= 18/72 + 18/72
= 36/72

So, when w = 3, P(2 men) is not greater than P(1 man and 1 woman)

IMPORTANT: Now that we've shown that P(2 men) is not greater than P(1 man and 1 woman) when w = 3, we can see that, as the value of w increases, the answer to the target question will always remain the same.

As such, statement 1 is SUFFICIENT

Statement 2: w < 6
Consider these two conflicting cases:

Case a: w = 1
P(2 men) = (6/7)(5/6)
= 30/42

P(1 man and 1 woman) = P(man selected 1st and woman selected 2nd OR woman selected 1st and man selected 2nd)
= P(man selected 1st and woman selected 2nd) + P(woman selected 1st and man selected 2nd)
= (6/7)(1/6) + (1/6)(6/7)
= 6/42 + 6/42
= 12/42

So, when w = 1, P(2 men) is greater than P(1 man and 1 woman)

Case b: w = 3
In statement 1, we already showed that, when w = 3, P(2 men) is not greater than P(1 man and 1 woman)

Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer = A

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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