Use the following setup for question
Both Nadia and Samantha are applying to insure their car against theft.Nadia lives in a secure neighborhood,where the probability of theft is 10%.Samantha lives in a lesser secure neighborhood where the probability of theft is 25%.Both Nadia and Samantha own cars worth $10,000,and are willing to pay $100 over expected loss for insurance.
-If the insurance company can successfully screen both Nadia and Samantha into appropriate contracts,it would earn
A)Between a zero and $200 loss
B)Between zero and $200
C)$3500 loss
D)$3500 gain

Question

​Use the following setup for question
Both Nadia and Samantha are applying to insure their car against theft.Nadia lives in a secure neighborhood,where the probability of theft is 10%.Samantha lives in a lesser secure neighborhood where the probability of theft is 25%.Both Nadia and Samantha own cars worth $10,000,and are willing to pay $100 over expected loss for insurance.
-If the insurance company can successfully screen both Nadia and Samantha into appropriate contracts,it would earn​
A)​Between a zero and $200 loss
B)Between zero and $200
C)$3500 loss
D)​$3500 gain

Quizplus · Accepted Answer

The expected loss for Nadia is 10% of $10,000, which is $1,000. She is willing to pay $100 over this, so $1,100. For Samantha, the expected loss is 25% of $10,000, which is $2,500. She is willing to pay $100 over this, so $2,600. The total amount they are willing to pay is $1,100 + $2,600 = $3,700. The actual expected loss for the insurance company is $1,000 (for Nadia) + $2,500 (for Samantha) = $3,500. Therefore, the insurance company stands to gain $200 ($3,700 - $3,500), making the correct answer between zero and $200.

​Use the Following Setup for Question

Use the Following Setup for Question