Question 681786: Dear Tutor,
I'm having a problem with expected value problems. This is one: At many airports, a person can pay only $1.00 for a $100,000 life insurance policy covering the duration of the flight. In other words, the insurance company pays $100,000 if the insured person dies from a possible flight crash; otherwise the company gains $1.00 (before expenses). Suppose that past records indicate 0.45 deaths per million passengers. How much can the company expect to gain on one policy? On 100,000 policies? Thank you very much
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! At many airports, a person can pay only $1.00 for a $100,000 life insurance policy covering the duration of the flight. In other words, the insurance company pays $100,000 if the insured person dies from a possible flight crash; otherwise the company gains $1.00 (before expenses). Suppose that past records indicate 0.45 deaths per million passengers. How much can the company expect to gain on one policy? On 100,000 policies?
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Gain values from company's point of view: $1 ;-$999,999
Probabilities of those gain value : 999,999.55/1000000; 0.45/1,000,000
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E(x) = [999,999.55 - 0.45)/1,000,000 = 0.99999999..
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On 100,000 people the company can expect to make 100000*0.999999999 = $99,999
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Cheers,
Stan H.
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