Randoml Picking Socks May Not Be the Best Spelling

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Yesterday I asked the following question. A drawer contains 4 blue socks, 6 gray socks, and 8 black socks. You randoml choose one sock, then another from the drawer. What is the probability that you choose 2 socks that match?

Since I meant randomly and not randoml, we decided the odds of picking a match on the first try was about 32%. Let's extend the problem a little bit.

If you hadn't picked a match the first time, I'm assuming you would pick again. What are the odds now? What would happen the third time? How long until you do find a match?