The question is as above. Draw a decision tree describing John\'s problem and hi

Question

The question is as above.

Draw a decision tree describing John's problem and his optimal decision and certainty equivalent.

John is an exchange student at SUN University. His room light has just burned out, and so he goes to the only store in the neighborhood to buy a replacement bulb. John requires a bulb for only six more months. In the store, John finds two boxes of light bulbs: In Box 1 are bulbs that are guaranteed to last at least 6 months, selling for S30 each. If John buys a bulb from Box 1 he can return to store for a free replacement if it burns out within six months. In Box 2 are bulbs with no warrantee, selling for $10 each. The store owner explains that all of the bulbs in Box 2 arc of the same type, and it is equally likely that they are either of Type A or of Type B. Type A bulb has a 0.5 probability that its lifetime is less than 6 months while Type B bulb has a 0.75 probability that its lifetime is less than 6 months. The store intends to dispose of Box 2 soon. Hence, if John buys a bulb from Box 2 and it bums out within 6 months, he must return and buy a bulb from Box 1. Draw a decision tree describing John's problem and his optimal decision and certainty equivalent.

Explanation / Answer

E (lightbulb from Box 2) is as below:

P(Type A bulb) = P(Type B bulb) = 0.5

P(lifetime less than 6 months given that its type A) = 0.5

P(lifetime less than 6 months given that its type B) = 0.75

P(bulb having lifetime less than 6 months given that its from box 2) =0.5*0.5+0.5*0.75 = 0.625

Now if the lifetime is less than 6 months John has to spend $10+$30 =$40 and if it is more than 6 months he just has to spend $10

E (lightbulb from Box 2) = 0.625*$40 +(1-0.625)*$10 = $28.75

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