Data Sufficiency

sl750 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.

Source : Magoosh

I'm a bit skeptical of this problem if the OA is D so will the OP please provide the answer given.

To find the probability, we just need to know the total number of black socks in the drawer.

Statement (1) tells us the fraction of socks in the drawer that are black. Combine that with the total number of socks given in the question and we know the exact number (4/9 of 36 or 16). From this we can calculate the probability. SUFFICIENT

Statement (2) tells us the relationship between black and white socks, BUT, without knowing that there are ONLY black and white socks in the drawer, we cannot calculate the actual number of black socks. INSUFFICIENT

**Note: if we DID KNOW that there are only black and white socks in the drawer, then black socks plus the white socks would = 36 socks. b+(b+4)=36 so 2b=32 or b=16, the same solution as statement (2). BUT we do not have information to guarantee that there are not other colors of socks in the drawer as well.

Therefore, the way this question is specifically worded means that the answer should be A.


Whit