Fred plans a major home improvement project that involves replacing the lighting fixtures in his living room. He is considering two kinds of fixtures, Model I and Model II. The work involved in installing the fixtures depends on the kind of wiring in the living room, and without tearing into the sheet rock this is unknown.
If the wiring is Type A, installing Model I fixtures is a 4 hour job, but if the wiring is Type B it will take 20 hours.
If the wiring is Type A, then Model II fixtures will take 16 hours, and if the wiring is Type B it will take 10 hours.
Obviously, Model I is best if it's Type A wiring, and Model II is best for Type B wiring. Fred thinks it equally likely that the wiring is of either type (i.e., both probabilities are 50%).
By drilling holes in the sheet rock and then repairing them, Fred figures he can do an inspection of the wiring and determine exactly what kind it is. If it's Type A he'll go with Model I, and otherwise he'll go with Model II. However, such a thorough check will take 4 hours.
He says to is wife, "It will take 4 hours to settle the issue. It's not worth it. I can get the whole job done in that time if it's Type A wiring. I'll go with Model I now and hope for the best".
(a) [This part should be fairly easy] Assume that time taken to complete the job is Fred's only concern - all other factors are equal. I.e., Fred's utility is directly proportional to the negative of time (less time equals more utility).
Draw a decision tree, then calculating expected values to check on the soundness of Fred's reasoning.
(b) [This part will be harder] Fred's wife Freda, who happens to be an electrician, suggests a compromise. "I can do a quick check of the wiring without drilling any holes. It will only take me 2 hours. There's an 80% chance I'll get it right, i.e., a 20% chance I'll get it wrong, but at least you can then make a more informed guess.
As he always does, Fred went along with his wife's suggestion. Was he right to do so? (Again, assume time is the only issue, and that pleasing his wife does not count)