# Clarification on simple a application of expected value

I am reading the following problem on expected value:

A car insurance company has determined the probabilities for various claims for drivers ages $$16$$ through $$21$$ as follows:

Claim amount Probability
$$\0$$ $$0.7$$
$$\2000$$ $$0.15$$
$$\4000$$ $$0.08$$
$$\6000$$ $$0.05$$
$$\8000$$ $$0.01$$
$$\10000$$ $$0.01$$

a) Calculate the expected value and describe what it means in practical terms.
b) How much should the company charge as an average premium so that it does not lose or gain money on its claim costs?

Concerning (a):
The expected value is calculated to $$\1100$$ which is just a direct application of the definition of the expected value.
Now does this mean that the insurance company should expect to pay on average $$\1100$$ per claim? Or that it should expect to pay in average $$\1100$$ per car insured i.e. to everyone insured in the age group of $$16$$-$$21$$?

Concerning (b):
I think that it should be that everyone in the age group of $$16$$-$$21$$ is charged $$\1100$$, right?

I woudl interpret as folows. Since $$0$$ Euro is a possible claim, "per claim" makes no sense, so one should expect to pay $$1100$$ Euro per car insured in the age group 16-21. So one should charge 1100$(per year probably, but this is not specified) from everyone. • Since 0 Euro is a possible claim, "per claim" makes no sense.$70\%$of the claims are for$\$0$ which I suppose is $\equiv$ of no claim. $1\%$ is claims of $\$10000$but the payout is neither, so wouldn't the$\$1100$ be the average per claim? – Jim May 28 at 10:38
• 1100 Euro is the average claim each insurance holder  so the expected value is for everyone in the age group? – Jim May 28 at 11:02
• It mentions few lines earlier before the problem description: For example, an insurance company can tally various claim amounts over many years. If $15\%$ of these amounts are for $\$2000$claim, then the probability of this claim amount is$0.15\$. So I think the table is an example of a gross recording over a long period of time (multiple years). But still it is unclear to me how the expected value should be interpreted, i.e. if it the average of all claims recorded over the past years, so it is the expected payout on average for each claim or is it it counted over the entire age group. – Jim May 28 at 10:43