LogFAQs > #877611596

The answer is 1/3.

The colour of the first sock drawn is not important; the second sock always has a 1/3 chance of matching it (since there will be two non-matching socks and one matching sock left in the drawer).

Note that drawing simultaneously does not affect this condition. If our socks are W1/W2 and P1/P2, the total combinations of socks that could be drawn are:

W1/W2
W1/P1
W1/P2
W2/P1
W2/P2
P1/P2

Two of the six combinations satisfy the requirement of matching, so the answer is still 1/3.

Zeus posted...

And again, I'll post the math: There are FOUR possible outcomes. It's either white/white, pink/pink, white/pink, or... well, white/pink again. To get it down to a 1/3 chance, you'd need to add additional unmatched socks.

Not so.

Well... I mean, you could say there's four possible outcomes (drawing white/white, white/pink, pink/white and pink/pink) and that's technically correct, but the problem is that not all of those draws are equally likely. The second and third of those combinations are twice as likely as the first and last.

Keep in mind, this isn't like "coin tosses", where the results are purely random. We are drawing from a sample and, thus, each draw affects the odds of subsequent draws. Basically, if I had a sock drawer with 100 white and 100 red socks, each white sock I draw increases the odds that subsequent draws will be red, because there are less white socks to draw. Contrast that where if I toss 100 coins, each heads result does NOT affect the odds of getting a subsequent tails.

In order for your answer to be correct, you would have to replace the sock you drew after you drew it. Basically you would draw a sock, note its colour, then return it to the drawer and draw again - your subsequent draw would have a 50% chance of being the noted colour and a 50% chance of being the opposite colour. But in the question as stated, where you draw a sock and keep it with you, the next draw will have a greater chance of being the opposite colour simply because there are now more of that colour to draw.
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