Bill and Ted are going to the beach with hopes of having an excellent adventure. Before going, they read a report by the world’s leading authority on tiger shark behavior indicating that when a tiger shark is in the vicinity of swimmers at the beach, there is a 0.20 probability of the shark biting a swimmer. Shortly after arriving at the beach and getting in the water, Bill and Ted spot the unmistakable dorsal fin of a tiger shark on the surface of the water in the vicinity of where they are swimming. Bill says to Ted, “Dude, let’s get out of the water, there’s a 0.20 probability someone is going to get bitten by that shark.” Ted replies to Bill, “You are way wrong, man! That probability could be zero. Chill out and enjoy the surf, dude.”

a. Show that Ted is correct about the probability. (Consider that P(A) = P(A ∩ B) +P(A ∩ B- ).

b. Suppose Bill and Ted decide to stay in the water and are bitten by the shark. Was staying in the water a good decision? Was the outcome of the decision good or bad?

c. Suppose Bill and Ted decide to stay in the water and are not bitten by the shark. Was staying in the water a good decision? Was the outcome of the decision good or bad?