## Pairs of Socks

1. A sock drawer contains some number of red and blue socks (and no other color.) In each case below, find the number of socks of each color in the drawer. A pair of socks is removed at random.
1. The probability they are both red is 1/3, and the probability they are both blue is 1/6.
2. The probability they are both red is 1/2, and the probability they are both blue is 1/12.
3. The probability they are both red is 1/2, and the probability they are both blue is 1/14.
2. Some number of green socks are now also in the drawer. Again, find the number of socks of each color in the drawer. A pair of socks is removed at random.
1. The probability they are both red is 1/3, and the probability they are both blue is 1/15.
2. The probability they are both red is 1/5, and the probability they are both blue is 1/15.
3. The probability they are both red is 1/6, and the probability they are both blue is 1/12.
4. The probability they are both red is 1/8, and the probability they are both blue is 1/12.
Note: The problems above are not necessarily listed in order of difficulty.

Source: Mensa's Nearly Impossible Baffling Brainteasers #36, plus original extensions.

Solution
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