A store has 80 modems in its inventory, 30 coming from Source A and the remainder from Source B. Of the modems in inventory from Source A, 20% are defective. Of the modems in inventory from Source B, 8% are defective.

Calculate the probability that exactly two out of a sample of five modems selected without replacement from the store’s inventory are defective.

• 0.010
• 0.078
• 0.102
• 0.105
• 0.125

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

Solution: C

The number of defective modems is 20% x 30 + 8% x 50 = 10.

The probability that exactly two of a random sample of five are defective is

[[math]] \frac{\binom{10}{2} \binom{70}{3}}{\binom{80}{5}} = 0.102. [[/math]]

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