Problem set 9 1/3 F S 1/3 1/6 FV 1/3 V. S release ard savs says Foo-foo Sauron Foo-foo"release released Define the events s, f, and"F"as follows F=Guard says Foo-Foo is released F= Foo-Foo is released s=Sauron is released The outcomes in each of these events are noted in the tree diagram Saurons error is in failing to realize that the event F(Foo-foo will be released) is dif Probability that Sauron is released, given that Foo-foo is released, is indeed 1 42 ular, the ferent from the event"F(the guard says Foo-foo will be released ). In partic Pr(S/p)sPr(S∩F Pr(F) ++ But the probability that Sauron is released given that the guard merely says so is still 2 /3 Pr(S"F) Pr(S∩“F Pr("F") 3 So Sauron s probability of release is actually unchanged by the guards statement Problem 4. You shuffle a deck of cards and deal your friend a 5-card handProblem Set 9 5 ￾ ￾ ￾ ￾ ￾ ￾ ❅ ❅ ❅ ❅ ❅ ❅ released ✟✟✟ ✟✟✟ ❍❍❍❍❍❍ guard says F, S F, V V, S 1/3 1/3 1/3 F F V V 1 1/2 1/2 1 1/3 1/6 1/6 1/3 prob. × × guard says ”Foo-foo” × × × Foo-foo released × × Sauron released Define the events S, F, and “F” as follows: “F” = Guard says Foo-Foo is released F = Foo-Foo is released S = Sauron is released The outcomes in each of these events are noted in the tree diagram. Sauron’s error is in failing to realize that the event F (Foo-foo will be released) is dif￾ferent from the event “F” (the guard says Foo-foo will be released). In particular, the probability that Sauron is released, given that Foo-foo is released, is indeed 1/2: Pr (S | F) = Pr (S ∩ F) Pr (F) = 1 3 1 3 + 1 6 + 1 6 = 1 2 But the probability that Sauron is released given that the guard merely says so is still 2/3: Pr (S | “F”) = Pr (S ∩ “F”) Pr (“F”) = 1 3 1 3 + 1 6 = 2 3 So Sauron’s probability of release is actually unchanged by the guard’s statement. Problem 4. You shuffle a deck of cards and deal your friend a 5-card hand