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When all factors are taken into account, an insurance company estimates that the probability of my father making a claim for damages to his pontoon boat for $5000 is 0.1, and that the probability of the pontoon boat being totally destroyed is .005. Should that tragedy happen, the company will have to pay $15,000. The company charges my father $1000 for the insurance policy. What is the expected value of this policy to my father?

Respuesta :

Answer:

The expected value of this policy is -$425.

Step-by-step explanation:

The probability distribution for the claim for damages is as follows:

 Amount to be received             Probability

$5,000 - $1,000 = $4,000            0.10

$15,000 - $1,000 = $14,000          0.005

              -$1,000                             0.895

              TOTAL                        1.000

Compute the expected value of this policy as follows:

[tex]E(X)=\sum x\cdot P(X=x) \\\\[/tex]

         [tex]=(4000\times 0.10)+(14000\times 0.005)-(1000\times 0.895)\\\\=400+70-895\\\\=-425[/tex]

Thus, the expected value of this policy is -$425.