18. Correct. The answer is true.
In order to calculate the probability of
having a commercial discovery in the area, we have to use the 'Theorem of Total
Probability' which tells us that the total probability of an event 'B' which is
conditional to the occurrence of events 'Ai' (Ai are
partitions of a set 'S' which contains all the possible events) is as follow:
As you can see, the theorem is a
generalization of the conditional probability theorem: P(A∩B)
= P(B/A)*P(A). See exercise 16. Applying this concept, we can calculate the
total probability of B:
P(B) = P(B|A1)*P(A1)
+ P(B|A2)*P(A2) + P(B|A3)*P(A3)
P(B) = (0.20)*(0.35) +
(0.25)*(0.2) + (0.2)*(0.45) = 0.21
There is a 21% probability of discovering oil
commercial reserves in the area.