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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

Respuesta :

Cricetus

Answer:

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

Explanation:

According to the given values in the question,

The expected value will be:

⇒ [tex]E(value) = Sum \ of \ (x\times P(x))[/tex]

By putting all the given values, we get

⇒                 [tex]=1000\times 0.05+5000\times 0.02+25000\times 0.01+0\times 0.92[/tex]

⇒                 [tex]=50+100+250+0[/tex]

⇒                 [tex]=400[/tex] ($)

As we can see that,

[tex]E(value)<premium[/tex]

[tex]400<1000[/tex]

Thus the above is the correct answer.

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