A company issues auto insurance policies. There are 900 insured individuals. Fifty-four percent of them are male. If a female is randomly selected from the 900, the probability she is over 25 years old is 0.43. There are 395 total insured individuals over 25 years old. A person under 25 years old is randomly selected.

Calculate the probability that the person selected is male.

• 0.47
• 0.53
• 0.54
• 0.55
• 0.56

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

Solution: B

The number of males is 0.54(900) = 486 and of females is then 414. The number of females over age 25 is 0.43(414) = 178. The number over age 25 is 395. Therefore the number under age 25 is 505. The number of females under age 25 is 414 – 178 = 236. Therefore the number of males under 25 is 505 – 236 = 269 and the probability is 269/505 = 0.533.

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