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December 31st, 2013, 07:18 AM   #1
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Insurance Policy Problem

Hi, I just encountered this question today and I cannot solve it. The question is:
Suppose the premium of a home insurance policy is $200 and in case of a fire the insurance company will pay out $200,000. Let X denotes the profit(or loss) of such a policy. X is a random variable. The expected value of X depends on a probability of a fire, p=0.0002.

If an insurance agent wants to sell such policy to you, will you buy the policy? why?

I really do not know how to proceed this question. This is the last part of the question and i already solved the previous parts.
Thank you very much
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December 31st, 2013, 09:34 AM   #2
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Re: Insurance Policy Problem

Converting it to fraction, the probability of a fire = 1/5000. Therefore if 5,000 policies are sold, the insurance company will collect $1,000,000 (1 million) and pay out $200,000 for an insurance company profit of $800,000, which is $160 per policy. Based on the probability of a fire, a policy should cost $40 and you should not buy the policy in question.
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December 31st, 2013, 10:10 AM   #3
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Re: Insurance Policy Problem

Quote:
Originally Posted by EvanJ
....a policy should cost $40 and you should not buy the policy in question.
Buy ok if $200 is a 5year premium
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