Question

Jill has a drawer that contains 8 pairs of matching socks, none of which match any of the other pairs. If Jill reaches blindly into her drawer and wants to guarantee she gets at least one pair of matching socks, what is the minimum number of socks she must pull out?

Answer 1

The minimum number of socks she must pull out is:

9

Explanation:

It is given that:

Jill has a drawer that contains 8 pairs of matching socks.

Now if Jill pulls out socks from her drawer then the minimum number of socks she need to pull out in order to ensure that she has at least one pair of matching socks is:

9

( since if she pulls out 8 socks then there may be a possibility that all of the 8 socks are distinct i.e. none of them come out in pair.

Now when she will draw the 9th sock then there is a surity that it will match with any of the previous 8 drawn sock )

Answer 2

There is a chance of 1/16*1/15 that she gets the specific socks pair according to laws of probability and the counting principle but thats not how it will work over here.

As we should be guaranteed that she gets the number of socks she obviously must take out around 9 socks as we are taking the worst case scenario where all the socks that come out are the different ones so the ninth sock must match any of the others.