SOLUTION: After studying all night for a final exam, a bleary-eyed student randomly grabs 2 socks from a drawer containing 9 black, 6 brown and 2 blue socks, all mixed together. What is the

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Question 314759: After studying all night for a final exam, a bleary-eyed student randomly grabs 2 socks from a drawer containing 9 black, 6 brown and 2 blue socks, all mixed together. What is the probability that she grabs a matched pair?
Answer by Edwin McCravy(20086) About Me  (Show Source):
You can put this solution on YOUR website!
After studying all night for a final exam, a bleary-eyed student randomly grabs 2 socks from a drawer containing 9 black, 6 brown and 2 blue socks, all mixed together. What is the probability that she grabs a matched pair?

She can grab two black socks any of 9C2 or 36 ways.
She can grab two brown socks any of 15 ways.
She can grab two blue socks 2C2 or 1 way.

So she can be successful in 36+15+1 or 52 ways

She can pick any two socks 17C2 or 136 ways.

The desired probability is 52%2F136, or 13%2F34.

Edwin