A drawer contains four pairs of socks, with each pair a different color. One sock at a time is randomly drawn from the drawer until a matching pair is obtained. Calculate the probability that the maximum number of draws is required.

• 0.0006
• 0.0095
• 0.0417
• 0.1429
• 0.2286

Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.

Solution: E

The maximum number of draws needed is 5. This can only happen if the first four draws produce four different colors. The first draw can be any sock. The second draw must be one of the 6 (of 7 remaining) that are different. The third draw must be one of the 4 (of 6) that are different from the first two. The fourth draw must be one of the 2 (of 5) that are different. The probability all of this happens is 1(6/7)(4/6)(2/5) = 0.2286.

Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.