The last sock out of the drawer

Question

A drawer holds 7 black socks and 3 white socks, 10 in total. You pull them out one at a time in the dark until the drawer is empty. What is the probability that the last sock pulled out is white?

Accepted Answer

The "last" sock feels special, but it is not. Every ordering of the 10 socks is equally likely, so the sock that ends up drawn last is a uniformly random one of the 10, exactly like the first. So the chance the last sock is white is the white fraction: P(	ext{last is white})=\frac{3}{10}=0.3. Takeaway. First and last positions are symmetric with every other position. The last sock being white has the same probability as the first sock being white: the overall fraction of white socks.

The last sock out of the drawer

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