Question 2 (40 points)Fisherman Fred has a decision problem. He is fishing at a lake that either has or does not have a nice juicy fish in it. He is an experienced fly fisherman and knows that if there is a fish in the lake, he has a probability 0.5 of catching it every time he casts. (If the fish is not there, he, of course, has probability zero of catching it. He figures that every cast takes 5 minutes, and if he catches a fish it will take him another 5 minutes to cook it on his burning camp fire. However, if he were to quit, he could drive into town to eat, but this would take K minutes (from the time he leaves until his food is served). Fred wants to minimize the expected time until dinner. Fred summons up all his past knowledge and concludes that P is the probability that the fish is in the lake. He has bait available for two possible casts, so he has three decision alternatives. Go to town right away, Cast once and go to town if no catch). . Cast twice and go to town if no catch), a. (15 points) Draw an influence diagram describing Joe's decision problem. b.(15 points) Draw a decision tree describing Joe's decision problem (Hint: you will have a single decision node in the tree). c. (10 points) Obtain an expression for the value of P as a function of K for which Fred would be indifferent between going to town right away or casting once and going to town if he doesn't catch a fish on the first try)