Pairs of Socks

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.

The probability they are both red is 1/3,
and the probability they are both blue is 1/6.

The probability they are both red is 1/2,
and the probability they are both blue is 1/12.

The probability they are both red is 1/2,
and the probability they are both blue is 1/14.
 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.

The probability they are both red is 1/3,
and the probability they are both blue is 1/15.

The probability they are both red is 1/5,
and the probability they are both blue is 1/15.

The probability they are both red is 1/6,
and the probability they are both blue is 1/12.

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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