This table shows claims and their probablity for an insurance company.
AMOUNT OF CLAIM PROBABILITY
$0 0.65
$50,000 0.25
$100,000 0.06
$150,000 0.02
$200,000 0.01
$250,000 0.01
1. Calculate the expected value?
2. How much should the company charge as an average premium so that it breaks even on its claim cost?
27,000
To calculate the expected value, you multiply each claim amount by its corresponding probability and sum up the results. Here's how you can calculate the expected value in this case:
1. Calculate the expected value:
Expected value = ($0 * 0.65) + ($50,000 * 0.25) + ($100,000 * 0.06) + ($150,000 * 0.02) + ($200,000 * 0.01) + ($250,000 * 0.01)
This simplifies to:
Expected value = $0 + $12,500 + $6,000 + $3,000 + $2,000 + $2,500
Expected value = $26,000
Therefore, the expected value is $26,000.
Now, let's move on to calculating the average premium for the insurance company to break even on its claim cost:
2. To calculate the average premium, you need to consider the expected value and the claim probability. The average premium is determined by dividing the expected claim cost by the probability of a claim.
Average premium = Expected value / Probability of claim
In this case, the probability of a claim is equal to 1 (or 100%), as every claim has a probability. Therefore, the average premium to break even on claim cost would be:
Average premium = $26,000 / 1
Average premium = $26,000
So, the company should charge an average premium of $26,000 to break even on its claim cost.
1. To calculate the expected value, we multiply each claim amount by its corresponding probability and sum the results.
Expected Value = ($0 * 0.65) + ($50,000 * 0.25) + ($100,000 * 0.06) + ($150,000 * 0.02) + ($200,000 * 0.01) + ($250,000 * 0.01)
= $0 + $12,500 + $6,000 + $3,000 + $2,000 + $2,500
= $26,000
So, the expected value of the claim is $26,000.
2. To determine the average premium that the company should charge to break even on its claim cost, we need to consider the probability of each claim amount. We can calculate the expected claim cost by multiplying each claim amount by its probability and summing the results.
Expected Claim Cost = ($0 * 0.65) + ($50,000 * 0.25) + ($100,000 * 0.06) + ($150,000 * 0.02) + ($200,000 * 0.01) + ($250,000 * 0.01)
= $0 + $12,500 + $6,000 + $3,000 + $2,000 + $2,500
= $26,000
To break even, the company should charge average premiums equal to the expected claim cost, which is $26,000.