shubhamkumar 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

OA: A

Prob. of selecting 2 men = 6C2/(6+w)C2 = 6*5/(6+w)*(5+w) ..........(1)

Prob. of selecting 1 men & 1 woman = 6C1*wC1/(6+w)C2 = 6*w/(6+w)*(5+w) ..........(2)

Comparing both probabilities

6*5/(6+w)*(5+w) > 6*w/(6+w)*(5+w) ?;

After cancellation, we get 5/2 > w

Brent@GMATPrepNow wrote:

shubhamkumar 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

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