Question

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.

Answer 1

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?

Answer 2

i'm assuming that every pair of socks is different

Answer 3

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

Answer 4

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

Answer 5

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