Question

(12pts) Acasa Insurance Company offers several plans for home insurance.

Plan A has a $700 yearly premium with a $3,000 deductible.
Plan B has a $1,200 yearly premium with a $1,000 deductible.
Water damage (from broken pipes, overflows, etc.) results in approximately 12% of claims overall, with an average claim being $5,200. What is the expected value (loss or gain) to Acasa for every customer who chooses plan A?


A) -$1,060

B) $436

C) -$360

D) -$100

Answer 1

The expected value to Acasa Insurance Company for every customer who chooses plan A is $436, which means on average, Acasa would make a gain of $436 per customer on this particular plan.

Step-by-step explanation:

To calculate the expected value (loss or gain) to Acasa Insurance Company for every customer who chooses plan A, we use the given probabilities and the average cost of a water damage claim. With a 12% chance of a claim and an average claim amount of $5,200, the expected cost to Acasa per claim is 0.12 * $5,200. If a claim occurs, Acasa pays the amount over the deductible, which is $5,200 - $3,000 = $2,200. The expected cost of claims per customer is thus 0.12 * $2,200. We must also subtract the yearly premium to find the expected value for Acasa.

The expected cost of claims per customer: 0.12 * $2,200 = $264.

The expected value for Acasa per customer taking plan A: $700 (premium) - $264 (expected cost of claims) = $436.

Answer 2

The answer is $436.

Step-by-step explanation:

The percentage of customers that have Plan A but don't make a claim is 88%, where those that do is 12%. Therefore you have to take into account all customers that have Plan A, those who claim and those who don't.

Those who don't claim lose $700 from paying their premium.

Those who claim gain $1500 from the payout.

$700 * (0.88) + -$1500 * (0.12)

$616 + -$180

$436