In a group of 25 factory workers, 20 are low-risk and five are high-risk. Two of the 25 factory workers are randomly selected without replacement. Calculate the probability that exactly one of the two selected factory workers is low-risk.

• 0.160
• 0.167
• 0.320
• 0.333
• 0.633

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

Solution: D

This is a hypergeometric probability,

[[math]] \frac{\binom{20}{1}\binom{5}{1}}{\binom{25}{2}} = \frac{20(5)}{25(24)/2} = \frac{100}{300} = 0.333, [[/math]]

Alternatively, the probability of the first worker being high risk and the second low risk is (5/25)(20/24) = 100/600 and of the first being low risk and the second high risk is (20/25)(5/24) = 100/600 for a total probability of 200/600 = 0.333.

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