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
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-> 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
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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):
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.
