The Smith sisters

In the Smith family there are some sisters, some of them having blue eyes.
If we pick at random two sisters, the chances they both have blue eyes is 1/2. How many sisters and how many have blue eyes ?

New : Socks

And another problem in the same vein :
In bulk in a drawer, I have some pairs of black and white socks. Alas I lost one sock. But picking two socks at random, the chances they are both white is 1/2.
What is the color of the sock I lost ? How many socks I have ?

Method and formulaes


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