1. An aerospace company has submitted bids on two separate federal gov- ernment defense contracts, A and B. The company feels that it has a 60% chance of winning contract A and a 30% chance of winning con- tract B. If it wins contract B, it believes that it has an 80% chance of winning contract A. a) [2] Are the events of winning contract A and winning contract B independent? Explain. b) [2] What is the probability that the company will win both con- tracts? c) [2] Are the events of winning contract A and winning contract B mutually exclusive? Explain. d) [2] What is the probability that the company will win at least one of the contracts? e) [2] What is the probability that the company will win neither con- tract? f) [2] What is the probability that the company will win contract A but not contract B? g) [2] If the company wins contract A, what is the probability that it will win contract B? h) [2] If the company wins contract B, what is the probability that it will not win contract A