How to calculate the probability of matching sock from a drawer? I'm not sure how to approach this problem from homework. The only equation I have for calculating probability is if each outcome in the sample space has an equal opportunity. The below isn't equal opportunity right?
A drawer contains 6 red socks, 4 green socks, and 2 black socks. Two socks are chosen at random. What is the probability that they match?
 A: Try starting here: What is the probability of drawing two red socks? Well, there are 6 red socks, and you need to choose two of them, meaning there are 6C2 (read "6 choose 2") ways to succeed, or 15 ways to draw two red socks. There are 12 total socks, and you choose 2, so there are 12C2 total combinations of 2 socks, or 66 total combinations of two. Since you have 66 possible combinations, and 15 of them are ways to succeed in drawing two red socks, the probability of drawing two reds is 15/66 or 22.7%. Hopefully you can take it from there.
A: Here are all the different ways of pairing one sock with another different one, arranged systematically:

"Random" in this context means that each pairing is equally likely.  Therefore, to find the probability of a color match, count the color-matched pairs and divide by the total.
Counting is made easier by noting that the color-matched socks occur within squares of $6$ by $6$, $4$ by $4$, and $2$ by $2$, and indeed the full tableau of pairings is a square of $12=6+4+2$ by $12$.  Within each square the diagonal is missing.  Thus, the number of pairs within any such square-without-diagonal of sides $k$ must be $k\times k - k = k(k-1)$.  Sum these values over the red socks ($k=6$), green socks ($k=4$), and blue socks ($k=2$), finally dividing by the total ($k=12$).
A general formula for any numbers of various kinds of socks follows immediately.
A: Here's what I got, P2red, 30/132 P2green, 12/132, P2black, 2/132, sum of 3 probabilities = 44/132 = 1/3, so 33.33% chance of matching, 66.66% chance of looking like a scrub
