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10) In your top dresser drawer are 6 blue socks and 10 grey socks, unpaired and mixed up. One dark morning you pull two socks from the drawer. What is the prob

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1 Answer

Since there are a total of 16 socks, the probability of both socks being blue is
P(blue) = 6/16 * 5/15 = 30/240 = 1/8

The probability of both being grey is
P(grey) = 10/16 * 9/15 = 90/240 = 3/8

The probability that they match is
P(blue) + P(grey) = 1/8 + 3/8 = 4/8 = 1/2


Very impressive! May I ask, just out of curiosity, where did the 5, 9, and 15 come from?
Kevin's correct. I'll just provide an assist. The first factor is the probability of drawing a blue (or grey) sock. Now, once that sock is gone, how many blue (or grey) socks remain, and how many socks are left in total? Because the first sock is removed, it changes the probability of drawing the second sock. Think of the second factor as the probability of drawing a sock of a certain color, given that one has already been pulled.