A drawer contains 10 red socks and 8 green socks. If two socks are randomly drawn from the drawer, what is the probability of getting a pair of red socks?
This is similar to the previous problem. The number of possible outcomes is the number of ways to draw 2 socks from the drawer: .
The number of favorable outcomes is the number of ways to pick two red socks: .
The probability of drawing a pair of red socks is then
which is all very well and good, but you just realized after all that nonsense that it's St. Patrick's Day and you need a pair of green socks instead. Doh!