Question

You have 10 pairs of socks,five black and five blue,but they are not paired up.instead they are all mixed up in a drawer.it is early in the morning and you do not want to turn on the light.
1. how many socks must you pull out to guarantee that you have a pair of one color?

2. how many must you pull out to have two good pairs(each pair is the same color)?

3. how many must you pull out to be certain that you have a pair of black socks? use a systematic approach to list all possible outcomes as a way to justify the answer in each case.

Answer 1

The answer for

1) 3 socks

2) 5 socks

3) 1 pair of socks

Explanation:

1) In the second trial, you choose one color, you say black, first, and second, say blue. The third sock you're taking out now has two black or brown. Therefore, you must draw at least 3 socks to ensure that you have a single color pair..

2) You get black first.

You're pulling out brown, second.

You tear down charcoal, Thrid.

Second, you cut out charcoal. (one pair complete)

Second, you're only heading out. (2 pairs full) Thus, you have to take out at least 5 socks to guarantee two pairs in the same colour.

3) You want 1 pair of black socks

The worst case is:  [ 5 blu ]

The 6th pick guarantees you will have 1 pair of black socks