An aerospace company has submitted bids on two separate federal government defense contracts, AandB . The company feels that it has a 60% chance of winning contract Aand a 30% chance of winning contractB . If it wins contractB , it believes that it has an 80% chance of winning contract A.
a) Are the events of winning contract A and winning contract B independent? Explain.
b) What is the probability that the company will win both contracts?
c) Are the events of winning contract A and winning contract B mutually exclusive? Explain.
d) What is the probability that the company will win at least one of the contracts?
e) What is the probability that the company will win neither contract?
f) What is the probability that the company will win contract A but not contractB?
g) If the company wins contract A, what is the probability that it will win contractB?
h) If the company wins contractB , what is the probability that it will not win contract A?
i) If the company does not win contract A, what is the probability that it will win contract B?