1: Conditional Probability Shortly before the attack on Pearl Harbor, a Japanese zero plane made a crash landing on an uninhabited island near Honolulu just before dawn. Alerted to the crash by smoke, American authorities in Hawaii had to act based on the following information: All the planes operating in the area are either American or Japanese - 90 percent were American and 10 percent were Japanese. Local fisherman identified the plane as American. It is well known that Hawaiian fishermen correctly identify things about 90 percent of the time. A) What is the probability that a randomly selected plane in the area would be American and that fisherman would correctly identify it as such? B) What is the probability that a randomly selected plane in the area would be Japanese and that a fisherman would incorrectly identify it as American? C) What is the probability that a randomly selected plane in the area would be identified by a fisherman as American? D) What is the probability that the plane was American, rather than Japanese, given that the fisherman identified it as American? E) General Short, leader of the forces in Hawaii, sees the estimate in (d) and is certain it must be an error. Assuming your answer for part (D) is correct, what bias/fallacy might the General be guilty of entertaining