# 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

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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) –  Listing Jun 25 '11 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. –  André Nicolas Jun 25 '11 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 $$\frac{4}{10}.$$

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