SOLUTION: A sock drawer contains 6 socks, 3 of which are definitely blue and the other 3 of which are either blue or black (exactly how many of each is unknown). If the probability of pickin

Question 320792: A sock drawer contains 6 socks, 3 of which are definitely blue and the other 3 of which are either blue or black (exactly how many of each is unknown). If the probability of picking two blue socks in a given random selection of two socks is 2 /3, how many black socks must the drawer contain?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Let

represent the number of blue socks in the drawer before the first selection is made. Then we know the probability of selecting a blue sock on the first trial is

. Given that a blue sock is selected on the first trial, we know that there are one fewer total socks and one fewer blue socks, hence the probability of drawing a blue sock on the second trial is:

. Then the overall probability of drawing two blue socks is given by:

A little algebra gets us to:

Hence:

Which factors to

Toss out the negative root (minus 4 blue socks? Ludicrous!) and we see that we must have 5 blue socks out of 6 at the start in order to be only 2/3 certain of drawing a pair.

John

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