Question

An actuary is a person who assesses various forms of risk. Based on past data, the holder of an automobile insurance policy pays an insurance premium of $1200 and has a 5% chance of an accident causing $1000 of damage, a 2% chance of $5000 damage and a 1% chance of totaling the car worth $25,000. The probability of the insurance holder making through the year without any accidents is 92%. Find the expected value and interpret it. Is the insurance company likely to make or lose money with this type of policy in the long run

Answer 1

With this policy throughout the long run, the insurance company will make money. A further explanation is provided below.

Step-by-step explanation:

According to the given values in the question,

The expected value will be:

⇒
`E(value) = Sum \ of \ (x* P(x))`

By putting all the given values, we get

⇒
`=1000* 0.05+5000* 0.02+25000* 0.01+0* 0.92`

⇒
`=50+100+250+0`

⇒
`=400` ($)

As we can see that,

`E(value)<premium`

`400<1000`

Thus the above is the correct answer.