# Possibility of getting odd pair socks

My son's drawer has 3 black socks and 2 white socks. He cannot understand that, when eyes closed and tries to get a pair, why in 1st attempt same color pair is never found, it is usually mismatched. what he does if pair is mismatched he throws back in the drawer ! He has asked me this few times.. I cannot answer him ...( we are not color blind!) thank you. Rodney

• 1. I think this is not real-analysis. 2. Draw a small tree chart and mark all cases you have and you already solved this. (Consider the probabilitys are not all equal) Jun 25, 2011 at 11:45
• Note that the probability of a match is not dramatically less than $1/2$. Perhaps the "usually mismatched" perception comes from the fact that we remember mismatches more than matches, just like we remember wrong weather forecasts more than right ones. Jun 25, 2011 at 13:10

There are $$\frac{5 \times 4}{1 \times 2} = 10$$ ways of choosing two socks from a drawer containing five socks. There are three ways of choosing a matching pair of black socks and one way of choosing a matching pair of white socks. Thus there are four ways of choosing a matching pair of socks. The probability of choosing a matching pair of socks is $$\frac{4}{10}.$$