An insurance company insures 100,000 cars in a certain area. The company has determined that on average, each year they will have to pay the following amounts for accidents in the area:
$100,000 with probability 0.0004
$50,000 with probability 0.001
$25,000 with probability 0.006
$5000 with probability 0.011
$1000 with probability 0.023

What is the company's expected payout per car each year?

A)$318.00
B)$4163.00
C)$4140.00
D)$381.60
E)$279.84

Question

An insurance company insures 100,000 cars in a certain area. The company has determined that on average, each year they will have to pay the following amounts for accidents in the area: ​
$100,000 with probability 0.0004
$50,000 with probability 0.001
$25,000 with probability 0.006
$5000 with probability 0.011
$1000 with probability 0.023
​
What is the company's expected payout per car each year?
​
A)$318.00
B)$4163.00
C)$4140.00
D)$381.60
E)$279.84

Quizplus · Accepted Answer

The expected payout per car each year is the sum of the products of the payout amount and the probability of that payout. So, the expected payout is:(100000 * 0.0004) + (50000 * 0.001) + (25000 * 0.006) + (5000 * 0.011) + (1000 * 0.023) = $318.00

An Insurance Company Insures 100,000 Cars in a Certain Area