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A drawer contains 36 socks, and 2 socks are selected at rand

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by rakeshd347 » Sat Oct 05, 2013 6:04 pm
A drawer contains 36 socks, and 2 socks are selected at random without replacement. What is the probability that both socks are black?

(1) The probability is 4/9 that the first sock is black.
(2) The number of white socks in the drawer is 4 more than the number of black socks.

OA is A
Last edited by rakeshd347 on Sat Oct 05, 2013 10:53 pm, edited 1 time in total.
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Source: — Data Sufficiency |
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by theCodeToGMAT » Sat Oct 05, 2013 8:38 pm
36 socks --> 2 are drawn

To find: Probability that both socks are black

Statement 1:
Probability = 4/9 = 16/36
So, 16 are Black
SUFFICIENT

Statement 2:
W = B + 4
No idea if the drawer contains socks of other color
INSUFFICIENT

Answer [spoiler]{A}[/spoiler]
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by [email protected] » Sun Oct 06, 2013 1:05 am
Hi rakeshd347,

This DS question can be easily solved with a bit of "probability math" and a bit of TESTing Values.

We're told that there are 36 socks, but we are told NOTHING about their color(s). The question asks if we pull 2 socks, what is the probability that they're both black.

Fact 1: Probability that first sock pulled is black is 4/9. We can figure out the total number of black socks:

36(4/9) = 16 black socks. This would give us enough information to calculate the probability of 2 black socks pulled:

(16/36)(15/35) = one answer; no reason to do the math.
Fact 1 is SUFFICIENT.

Fact 2: The Number of White socks is 4 more than the Number of Black socks.

W = B + 4

If W = 4, B = 0, the probability of pulling 2 black socks is 0

If W = 6, B = 2, the probability of pulling 2 black socks is something other than 0
Fact 2 is INSUFFICIENT

Final Answer: A

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