posted by kim .
There are 6 pairs of black socks and 6 pairs of white socksWhat is the probability to pick a pair of black or white socks when 2 socks are selected randomly in darkness?M
I think it's nCk which the total of socks would be 12 since we have 6 whites and 6 black. you would have to choose 2. in that case order does not matter and we use the combination formula 12C2 = 66 possible ways.
could be either BB or WW
Prob(BB) = (6/12)(5/11) = 5/22
which is the same as the prob(WW)
so prob of either WW or BB = 2(5/22) = 10/22
(note only other cases are WB and BW
and the prob of those = 2(6/12)(6/11) = 2/11 or 12/22
and prob of all cases = 10/22 + 12/22 = 22/22 = 1 )
All is good!
correction in 3rd last line, should be
and the prob of those = 2(6/12)(6/11) = 6/11 or 12/22