Question

8) There are three pairs of socks of three different types A, B, and C in a drawer. The goal is to pair these socks. If socks are pulled out two at a time and put back if not matching, what is the maximum number of times repeating this process until the socks are paired?

Answer 1

Answer: 2

I'm really struggling with this concept, hoping you guys could help me out.

The pairs have been separated out and you must take out a pair of socks.

Consider these problems and provide a calculation for each:

Probability of drawing a matching pair if you randomly draw 2 socks?

Probability of drawing a matching pair if you randomly draw 3 socks?

(Repeats up to randomly drawing 5 socks)

For 2 socks I got the following:

40 possible socks * 39 other possible socks = 1560 possible combinations of socks / 2 (to remove duplicate matches) = 780

For each set of socks, there are 8. 8 * 7 (7 other socks to each being matched) = 56 possible combinations in each set of socks / 2 to remove duplicates = 28 possible combinations of socks in each set.

28 / 780 = 0.036 probability of drawing a pair when drawing 2 socks from the drawer.

Step-by-step explanation: