SOLUTION: Your Sock drawer has six white socks, six brown socks, and for black socks. You randomly pick two socks and get a matching pair of black socks. Find the probability of this occurri
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Question 1163157: Your Sock drawer has six white socks, six brown socks, and for black socks. You randomly pick two socks and get a matching pair of black socks. Find the probability of this occurring. Found 3 solutions by ikleyn, solver91311, greenestamps:Answer by ikleyn(52754) (Show Source):
In all, there are 6 + 6 + 4 = 16 socks in the drawer.
The probability to get first sock black is .
The probability to get the second sock black is then .
The overall probability is the product P = = = = 0.05. ANSWER
Presuming you meant "four" black socks rather than "for" black socks as you wrote, it should be clear that, for the first draw, there are four outcomes that you would consider a success out of sixteen total outcomes -- giving you the probability that you draw a black sock on the first draw. Presuming that you were successful on the first draw, how many socks would remain in the drawer and how many of those would be black. Those numbers will give you the probability of drawing a black sock on the second draw. Since these two events are independent because you accounted for the possibility of the first sock being black when you calculated the probability of the second sock being black, the total probability is the product of the probabilities of the two individual events.
John
My calculator said it, I believe it, that settles it
Tutor @ikleyn showed an elementary way to solve this kind of problem, by looking at the probability of picking two black socks one at a time.
You should know and understand that method for solving the problem.
For more complex problems, a more sophisticated solution method might be required. You should know that other method, demonstrated below, for solving this problem.
You are choosing 2 socks out of a drawer containing 16 socks. The number of ways you can do that is "16 choose 2":
The outcome you want is choosing 2 of the 4 black socks. The number of ways you can do that is "4 choose 2":
The probability that you get 2 black socks is then
Often, in more complicated problems, it is helpful to be more complete in describing the desired outcome. For this problem, the desired outcome is choosing 2 of the 4 black socks, AND choosing 0 of the 6 white socks, AND 0 of the 6 brown socks. Then the calculation of the probability of getting 2 black socks is
