An auto insurance company has 10,000 policyholders. Each policyholder is classified as

1. young or old;
2. male or female; and
3. married or single.

Of these policyholders, 3000 are young, 4600 are male, and 7000 are married. The policyholders can also be classified as 1320 young males, 3010 married males, and 1400 young married persons. Finally, 600 of the policyholders are young married males.

Calculate the number of the company’s policyholders who are young, female, and single.

• 280
• 423
• 486
• 880
• 896

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

Solution: D

Let [math]N(C)[/math] denote the number of policyholders in classification [math]C[/math] .

Then

[[math]] \begin{align*} N(Young ∩ Female ∩ Single) &= N(Young ∩ Female) – N(Young ∩ Female ∩ Married) \\ &= N(Young) – N(Young ∩ Male) – [N(Young ∩ Married) – N(Young ∩ Married ∩ Male)] \\ &= 3000 – 1320 – (1400 – 600) \\ &= 880 . \end{align*} [[/math]]

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