Data Sufficiency

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

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

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?

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.

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 ?

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!

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.