LogFAQs > #877593546

Lokarin posted...

streamofthesky posted...

dancer62 posted...

Tails 64 posted...

I think it's 1/3. Imagine he picks a white sock. There are now 2 pink socks (non-matching) and 1 white sock, leaving a 1 in 3 chance of a matching pair.

Agree. It doesn't matter which he draws first, the chance of drawing a matching sock is 1/3.

Also agreed. Doesn't matter if he draws them simultaneously or not, for the purposes of the problem, you can treat one draw as the "first."

Whichever color he draws first, there are now three socks left. One is the matching color, two are not. Therefore, the probability he will draw a match is 1/3.

But you are forgetting to multiply by the odds of picking the first sock.

If you pick pink, you have 1/3 of getting pink again.
If you pick white, you have 1/3 of getting white again.
It's 1/3 regardless.

But fine, let's look at it your way.
You have a 1/2 chance of the first pick being white. And a 1/3 chance after that of the 2nd pick being white. 1/2 * 1/3 = 1/6 chance.
You have a 1/2 chance of the first pick being pink. And a 1/3 chance after that of the 2nd pick being pink. 1/2 * 1/3 = 1/6 chance.

1/6 + 1/6 = still 1/3 probability of getting matching colors.