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, without replacement. What is the probability that the two socks match?
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