1. ## challenging probability problem

A drawer has red socks and black socks. You take two socks out at random and the probability that both are red is exactly 1/2. How many socks are in the drawer?

2. Originally Posted by acc100jt
A drawer has red socks and black socks. You take two socks out at random and the probability that both are red is exactly 1/2. How many socks are in the drawer?
Well this probability is:

$\displaystyle P(r,r)=\frac{n_r}{N}\times \frac{n_r-1}{N-1} = 1/2$

Trial and error shows that $\displaystyle n_r=3,\ N=4$ is a solution, but is
it the only solution?

RonL