A drawer contains 8 black socks and 8 white. Two are pulled out randomly: I) probability that it is the same colour? II) how many will have to be pulled out for matching pairs?

1 Answer
Shwetank Mauria
May 9, 2018

(I) #7/15#; (II) #3# socks.

Explanation:

Let #B# denote pulling out a black sock and #W# denote pulling out a white sock from the drawer.

When two socks are pulled out randomly, the possibility that they are of same color would be when we pull out #BB# or #WW#.

(I) As there are #8# black socks and #8# white socks,

the probability of pulling out one black sock is #8/16# and pulling out another black will be #7/15#, as we are left with #15# socks with #7# black socks.

Hence probability of pulling out pair of black socks is #8/16xx7/15=7/30#

Similarly probability of pulling out pair of white socks too is #8/16xx7/15=7/30#

and hence the probability that it is the same color is #14/30=7/15#

(II) We must pull out three socks so that they are matching pairs. Observe that in such a case even if first two socks (if they are of same color, we are done) are of different colors, third must be of either color and we have got a matching pair.

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