Arman B. answered • 05/19/19
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The probability of picking a black sock is 6/14, as initially there are 6 black socks out of a total of 14. After a black sock has been picked, now there are 5 black socks left out of a drawer with 13 total socks. Therefore, the total probability is P = P1*P2, where P1 = 6/14 and P2 = 5/13.
So the final probability is:
6*5/(14*13) = 15/91 ~ 16.5%
Arman B.
tutor
Sure, good point. More possible scenario is that left pairs and right pairs are distinguishable, and if we assume nothing about additional patterns, we only have 3 remaining black socks that are a match. For example, if we had initially picked a right pair, then we need a left pair black sock, or vice versa.
So, another possibility given the distinguishability of left and right socks is (6/14)*(3/13) =9/91
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05/19/19
Joe M.
I’d agree. The only possible exception (question isn’t entirely clear) might be if not all the black socks match each other (there are 3 pairs of black socks and each has different shapes/patterns from the other black pairs). Then after drawing the first black sock P1 = 6/14, then the only way to match it is to draw its mate from the remaining 13, so P = P1*P2 = 6/14 * 1/13 = 6/182 = 3/91 or 3.3%. This to me is a less likely answer.05/19/19