Question 4 The probability that Amy watches a movie is 0.4. The probability that Susan watches a movie is 0.5. The probability that Amy watches a movie, given that Susan does, is 0.7". a) Find the probability that both Amy and Susan watch the movie. b) Find the probability that Susan watches the movie, given that Amy does. c) Do Amy and Susan watch the movie independently of each other? Justify your answer. d) Find the probability that either Amy or Susan watches the movie. Question 5 In a study by Department of Geography, they reported the following information. Of 100 past sites that were drilled and produced no oil, 91 gave a low reading. Of the 400 past sites that were drilled and produced some oil, 16 gave a low reading. Of the 300 past sites that were drilled and produced much oil, 3 gave a low reading. Given P(no oil) = 0.7, P(some oil) = 0.2 and P(much oil) = 0.1, calculate the probabilities of no oil, some oil, and much oil, given a low reading. 1|Dage Question 6 a) According to a record of from Department of Physics, the probability of a failure in a single mission of the Space Shuttle was lf600000. Using this value of p and assuming all missions are independent calculate the probability of at least one mission failure in 25 attempts. b) How small must p be made in order to ensure that the probability of no mission failures in 25 attempts is 0.999