How is this probability reasoning wrong?? 1. The problem statement, all variables and given/known data 2. Relevant equations The professor didn't say it explicitly, but I'm pretty sure that sock choices are taken to be independent, so P(A,B,C) = P(A)P(B)P(C). 3. The attempt at a solution The last part is easy...the correct probability is P(three socks of the same color) = P(all light) + P(all dark) = 1/2*1/2*1/2 + 1/2*1/2*1/2 = 1/4. But I CANNOT figure out where Francis's reasoning is wrong. I've been thinking about it for so long... He seems to be completely right, I mean, when you grab 3 socks you ALWAYS end up with 2 matching socks, and the probability of the other sock matching those two is 1/2...right? So from that reasoning the probability of all socks matching is 1/2. I've thought about it and thought about it and thought about it and I can't figure it out! It's driving me crazy!!! If you can find the flaw I would really appreciate it if you could please explain it or give me some good hints. Thanks to anyone who responds.