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Ambiguous DS :(

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Ambiguous DS :(

by Night reader » Wed Jan 05, 2011 4:09 pm

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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

any answer is acceptable, as long as it fits the logic
it says A, whereas I arrived to D :(
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by anshumishra » Wed Jan 05, 2011 4:13 pm

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Night reader wrote: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

any answer is acceptable, as long as it fits the logic
it says A, whereas I arrived to D :(
I think statement 2 may imply that there may be socks having colors other than white and black. Hence statement 2 is insufficient.

clearly A is sufficient, Hence A
Last edited by anshumishra on Wed Jan 05, 2011 4:36 pm, edited 2 times in total.
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by Oneva » Wed Jan 05, 2011 6:58 pm

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Hi I wasn't sure about the second choice as well. If taken at face value I would have assumed 20 white socks and 16 black socks.

But I was wondering if you could clarify how to reach the answer A? Sorry but I wasn't sure if what I did was correct.

I was thinking the first sock had a probability of 4/9 so essentially it was 16/36, then I would multiply by 15/35 to get the probability of 12/63. Was this the same answer?
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by anshumishra » Wed Jan 05, 2011 7:09 pm

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Oneva wrote:Hi I wasn't sure about the second choice as well. If taken at face value I would have assumed 20 white socks and 16 black socks.

But I was wondering if you could clarify how to reach the answer A? Sorry but I wasn't sure if what I did was correct.

I was thinking the first sock had a probability of 4/9 so essentially it was 16/36, then I would multiply by 15/35 to get the probability of 12/63. Was this the same answer?
Yes. I didn't calculate, as I knew it could be calculated. However, if you are interested to get the value, you are right. It would be 16/36*15/35.
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by bblast » Thu Jan 06, 2011 5:01 am

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Your answer is right night reader is we consider the question stating that the box only has white and black socks.

Agree that the question in ambiguous, whats the source ?
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by Superduperstudent » Fri Jan 07, 2011 9:07 am

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Night reader wrote: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

any answer is acceptable, as long as it fits the logic
it says A, whereas I arrived to D :(
Hi Night reader,

The problem is not so ambiguous. Answer D (Each statement alone is sufficient to answer the question) can not be correct because from statement 2 we know only that there are 4 more white socks than black sox in the drawer. There could be 5 white socks and 1 black sock. Because it is not GIVEN that there are ONLY white and black socks, this is not sufficient information to answer the question.

You are right, though, that statement 1 is sufficient. Calculating it is not necessary, that will just cost you time.

Good luck!
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by prat_agl » Sun Dec 09, 2012 12:17 pm

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A. probability of 1st black = total black socks / 36 = 4/9
Total black socks = 16. Hence sufficient.

B. There can be other socks as well so not sufficient.
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