An oil exploration company currently has two active projects, one in Asia and th
ID: 3351315 • Letter: A
Question
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) = 0.9 and P(B) = 0.8.
(1) If the Asian project is not successful, what is the probability that the European project is also not successful?
Explain your reasoning. Which of the following is correct?
(a) Since the events are not independent, then A' and B' are mutually exclusive.
(b)Since the events are independent, then A' and B' are mutually exclusive.
(c)Since the events are independent, then A' and B' are not independent.
(d)Since the events are independent, then A' and B' are independent.
(2) What is the probability that at least one of the two projects will be successful?
(3) 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.)
Explanation / Answer
a)
P(A) =0.9
P(B) =0.8
Since both are independent events,so A' and B' are also independent
choice D
P(B'|A') =P(B') =1-P(B) =1-0.8 =0.2
b) P(A') =1-P(A) =1-0.9 =0.1
P( atleast one is successful ) =P(AuB) =1-P(none is successful)
= 1- P(A' n B')
=1- P(A')*P(B') [ because A' and B' are independent events]
=1-(0.1)*(0.2)
= 1-0.02
=0.98
c) P[(A n B') | (A U B) ] = P[ (A n B') n (A U B)]/P(AuB)
=P(AnB')/P(AuB)
= [P(A) -P(AnB)]/P(AuB)
=[P(A) -P(A)*P(B)]/P(AuB)
=[0.9 -0.9*0.8]/(0.98)
=(0.9-0.72)/0.98
=0.18/0.98
=0.18367