Question

The robot in Futurama, Bender, has insured several of his body parts. His arms, legs, and head are insured. His policy costs a total of $1000 a year, and pays out $10000 if he loses his legs, $25000 is he loses his head, and $50000 if he loses his arms.

(a) List the sample space for the outcomes of Bender’s damages. Note that it is possible he loses both his legs and arms simultaneously, and so on. Sadly, the policy indicates that Bender may only claim one specific damage, so no combinations of arms AND legs simultaneously, and such.

(b) List the outcomes for what Bender can claim on his insurance policy. Finally, Bender places the probability of him claiming damages on his legs at 0.025, his head at 0.015, and his arms at 0.01. The rest of the time, he will make no claims on his policy.

(c) Find Bender’s expected value for this insurance policy.

(d) How much extra should Bender be willing to pay for this policy (assuming he will not buy it when he no longer gains a profit from the policy)?

Answer 1

a) The sample space of outcomes of Bender’s damages = {Arms, Legs, Head, Arms and Legs, Arms and Head, Legs and Head, Arms, Head and legs}

b) Bender can claim policy for only one of the damages that has occured to him. He can either claim for arms, either for legs or for head.

c) Expected value of the insurance policy =

= 0.025*10000 + 0.015*25000 + 0.01*50000

= $250 + $375 + $500

= $1125.

d)Bender pays $1000 for the policy, whereas, the expected value of the policy is $1125.

So, the extra amount the Bender would be willing to pay is $1125 - $1000 = $125.

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