There are 6 pairs of black socks and 6 pairs of white socks.What is the probability to pick a pair of black or white socks when 2 socks are selected randomly in darkness.
My thoughts:
Since there have asked for probability to pick a "pair", we must consider those same colored socks with a right and left sock.
So we have 6 Black right socks and 6 Black left socks.
Similarly 6 white right and 6 white left socks.
So the probability according to me is 6/24 * 6/23 + 6/24 * 6/23 = 3/23
(Probability of a pair of Black socks + Probability of a par of White socks)
However there is another approach: (6C1 * 6C1)/ 24C2 + (6C1 * 6C1)/ 24C2 = 6/23
Which is the correct approach and why? Why am I getting different results?