A generator can fail because of a fault either at unit termi

A generator can fail because of a fault either at unit terminals or at excitation system. Let A and B denote these two failure events. Suppose that the probabilities of the two events of failure are P(A) =p, and P(B) =q, and that the probability that both events will occur simultaneously is P(AB)= r. Determine the following probabilities.

-The probability that the generator will fail because of unit terminal fault only.

-The probability that the generator will fail because of excitation system problem only.

-The probability that the generator will not fail as a result of either of these two causes.

-The probability that the failure will be the result of only one of these two causes.

Solution

-The probability that the generator will fail because of unit terminal fault only.

P(A) - P(A and B ) = p - r

-The probability that the generator will fail because of excitation system problem only.

P(B) - P( A and B) = q-r

-The probability that the generator will not fail as a result of either of these two causes.

P(AUB) \' = 1 - P(A U B) = 1 - [ p+q-r] = 1 - p -q + r

-The probability that the failure will be the result of only one of these two causes.

P(A or B ) = p + q - r