Answer:
a) P(B'|A') = P(B') = 1 - 0.7 = 0.3.
The reasoning is that: since, events A and B are independent, then, events A' and B' are also independent and for independent events, P(A|B) = P(A).
b) P(A u B) = 0.82
c) P[(A n B')|(A u B)] = 0.146
Step-by-step explanation:
P(A) = 0.4
P(B) = 0.7
A and B are independent events.
P(A') = 1 - 0.4 = 0.6
P(B') = 1 - 0.7 = 0.3
a) If the Asian project is not successful, what is the proba- bility that the European project is also not successful?
P(B'|A') = P(B') = 1 - 0.7 = 0.3
The reasoning is that: since, events A and B are independent, then, events A' and B' are also independent and for independent events, P(A|B) = P(A).
b) The probability that at least one of the two projects will be successful = P(A u B)
P(A u B) = P(A) + P(B) - P(A n B) = 0.4 + 0.7 - (0.4)(0.7) = 0.82
OR
P(A u B) = P(A n B') + P(A' n B) + P(A n B) = (0.4)(0.3) + (0.6)(0.7) + (0.4)(0.7) = 0.82
c) Given that at least one of the two projects is successful, what is the probability that only the Asian project is successful?
P[(A n B')|(A u B)] = }P(A n B') n P(A u B)]/P(A u B) = P(A n B')/P(A u B) = (0.4)(0.3)/(0.82)
P[(A n B')|(A u B)] = 0.146
Hope this Helps!!!
