## xEnOnn 3 years ago Suppose there are 10 different pairs of socks in a drawer. In other words, there are 20 singleton socks in total in the drawer. I randomly pick 2 socks out from the drawer. What is the probability that the 2 socks that I picked out is a matching pair? My answer to this question is 1/2. But I am not sure if what I have done is correct because 1/2 seems quite unbelievable.

1. cwrw238

after picking out the first sock there are nine different pairs of socks and one which matches the first sock so i would think the chance of picking a matching one is 1 /19 ???? does that make sense?

2. cwrw238

i'm assuming that every pair of socks is different

3. xEnOnn

There are 20 socks in there, all of which are equally likely. How could it be only 1/19?

4. cwrw238

yes - but don.t you want a matching pair?

5. cwrw238

and aren't the pairs all different suppose we denote each pair by a number: 11 22 33 44 55 66 77 88 99 00 suppose the first sock we pick is 4 we are now left with 11 22 33 4 55 66 77 88 99 00 - we have to pick out the 4 to get a match and probability of picking this is 1/19