SOLUTION: A drawer contains a mixture of 12 black socks, 8 white socks, and 4 red socks. You randomly select 2 socks to wear. Determine the probability that you pick a matching pair. (Give y

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Question 1042797: A drawer contains a mixture of 12 black socks, 8 white socks, and 4 red socks. You randomly select 2 socks to wear. Determine the probability that you pick a matching pair. (Give your answer as a fraction.)
Answer by ikleyn(52879) About Me  (Show Source):
You can put this solution on YOUR website!
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A drawer contains a mixture of 12 black socks, 8 white socks, and 4 red socks. You randomly select 2 socks to wear.
Determine the probability that you pick a matching pair. (Give your answer as a fraction.)
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Successive outcomes:


1)  2 black socks of 12:  C%5B12%5D%5E2 = %2812%2A11%29%2F2 = 66;

2)  2 white socks of 8:   C%5B8%5D%5E2  = %288%2A7%29%2F2  = 28;

3)  2 red socks of 4:     C%5B4%5D%5E2  = %284%2A3%29%2F2  =  6.


The total space of outcomes:  C%5B12%2B8%2B4%5D%5E2 = C%5B24%5D%5E2 = %2824%2A23%29%2F2 = 12*23.

Answer.  %2866%2B28%2B6%29%2F%2812%2A23%29. Please calculate it on your own.