## Related questions with answers

An auto insurance company has 10,000 policyholders. Each policyholder is classified as: (i) young or old; (ii) male or female; and (iii) 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. How many of the company's policyholders are young, female, and single? Choose one of the following. (a) 280 (b) 423 (c) 486 (d) 880 (e) 896

Solution

VerifiedDefine sets:

$Y$ : young ( $Y^{\prime}$ : old),

$M$ : male $(M^{\prime}$ : female)

$R$ : maRried $(R^{\prime}$ : single)

Draw a three set Venn diagram with sets Y, M, S.

Fill from the inside out. The intersection of all three has 600.

the rest of $Y\cap M$ is 720, so the total of that intersection is 1320

the rest of $Y\cap R$ is 800,

the rest of $M\cap R$ is 2410.

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