A system consists of two components. The probability that the second component functions in a satisfactory manner during its design life is .9, the probability that at least one of the two components does so is .96, and the probability that both components do so is .75. Given that the first component functions in a satisfactory manner throughout its design life, what is the probability that the second one does also?

Answer : Step 1 : So far I have this setup: Let C1 be event 1st component is satisfactory. Let C2 be event 2nd component is satisfactory. P(C1 or C2) = 0.96 P(C1 and C2) = 0.75 P(C2) = 0.9 Are the two events it's asking about independent of each other. P(C1 or C2) = P(C1) + P(C2) - P(C1 and C2) So we have to find P(C1). P(C1) =...