SOA PROBLEM

[INTERESTEDSTUDENT]

An auto insurance company has 10,000 policyholders. Each policyholder is classified as(a) young or old;(b) male or female; and(c) married or single.Of these policyholders, 3000 are young, 4600 are male, and 7000 are married. The policyholderscan 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’spolicyholders who are young, female, and single.

I tried to do this exercise using exclusion and inclusion principle, but i couldn´t do it.

 

[Deleted member 4993]

An auto insurance company has 10,000 policyholders. Each policyholder is classified as(a) young or old;(b) male or female; and(c) married or single.Of these policyholders, 3000 are young, 4600 are male, and 7000 are married. The policyholderscan 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’spolicyholders who are young, female, and single.

I tried to do this exercise using exclusion and inclusion principle, but i couldn´t do it.

Please share your work with us - even if you think it is incorrect.

Please explain why do you think it was incorrect.

 

[BigBeachBanana]

Good old P exam. I took that 2 years ago.
The goal is to find [imath]Y \cap M' \cap C'[/imath] (Young, Female, and Single)
Start with finding [imath]Y\cap M'[/imath]. (Young and Female)
[math]Y=(Y\cap M) + (Y\cap M')[/math]Next, find [imath]Y\cap M' \cap C[/imath] (Young, Female, Single)
[math]Y\cap C=(Y\cap C \cap M)+(Y\cap C \cap M')[/math]Lastly, find [imath]Y \cap M' \cap C'[/imath]
[math]Y \cap M'= (Y \cap M' \cap C)+(Y \cap M' \cap C')[/math]