probability applications of count

Question

mixed in a drawer are 4 blue socks, 8 white socks, and 8 gray socks. you pull out two socks, one at a time, without looking. find the probability of getting 2 socks of the same color.

Answer 1

There are several ways of calculating this. One involves finding all the different ways (combinations, not permutations) of getting either two blue, two white, or two grey socks and divide by all the different combinations of 2 socks out of a drawer of 20 socks. Divide one by the other and voi la!

I prefer expected value calculations for the probability of success.

Given my first sock is blue, the probability of getting another blue is 3/19

Given my first sock is white, the probability of getting another white is 7/19

Given my first sock is grey, the probability of getting another grey is 7/19

The chances of getting a blue sock first is .2. The chances of getting a grey or white sock first is .4

The expected probability of success (2 socks) is found by adding all the conditionals up.

.2 * (3/19). +. .4 * (7/19) + .4 * (7/19). Which is .3263.