. Reconsider the credit card scenario of Exercise 52, and show that A and B are dependent first by
using the definition of independence and then by verifying that the multiplication property does
not hold.
. An oil exploration company currently has two active projects, one in Asia and the other in
Europe. Let A be the event that the Asian project is successful and B be the event that the
European project is successful. Suppose that A and B are independent events with P(A) ¼ .4 and
P(B) ¼ .7.
(a) If the Asian project is not successful, what is the probability that the European project is
also not successful? Explain your reasoning.
(b) What is the probability that at least one of the two projects will be successful?
(c) Given that at least one of the two projects is successful, what is the probability that only the
Asian project is successful?