Question

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.

Answer 1

about 0.53

Explanation:

54% of the insured, or .54×900 = 486 individuals are males. That leaves 900-486 = 414 that are females. 43% of those, or .43×414 = 178 are over 25, so the remainder of the 395 who are over 25 are male.

Since 395 -178 = 217 of the males are over 25, there are 486 -217 = 269 who are under 25. Then the fraction of insureds who are under 25 that are male is ...

269/(900 -395) = 269/505 ≈ 0.53

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It can be useful to make a 2-way table from the given information.