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) = 0.2 and P(B) = 0.6.

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? (Round your answer to three decimal places.)

a. Since A and B are independent events, the probability of failure in the Asian project does not interfere in the European project. Therefore, the probability that the European project is also not successful is:

[tex]P(B=not) = 1 - P(B) = 1-0.6 =0.400[/tex]

b. The probability that at least one of the two projects will be successful is given by the probability of A being successful plus B being successful minus the probability of both being successful:

[tex]P = P(A)+P(B) - P(A\cap B)=0.2+0.6-(0.2*0.6)\\P=0.680[/tex]

c. The probability that only the Asian project is successful given that at least one of the two projects is successful is:

[tex]P=\frac{P(A) - P(A\cap B)}{0.68}=\frac{0.2-0.2*0.6}{0.68}\\P=0.118[/tex]