A system consists of two components. The probability that the second component f

Question

A system consists of two components. The probability that the second component functions in a satisfactory manner during its design life is 0.9, the probability that at least one of the two components does so is 0.96, and the probability that both component do so is 0.75. Give that the first component functions in a satisfactory manner throughout its design life, what is the probability that the second one does so?

So far I have this setup:
P(Component B Success) = .9
P(Component A OR B Success) = .96
P(Component A AND B Success) = .75

Are the two events it's asking about independent of each other since A = success, so what is the success of B? I'm not sure how to set this up/not sure I fully understand the question. An explanation + the process of solving this would be greatly appreciated, thank you.

Explanation / Answer

Ah-ha, I was able to solve this after looking at it and thinking about it for a while. For others to reference, solve for P(A), by:

P(A U B) = .96

P(A intersection B) = .75

We know that P(A) + .9 - .75 = .96

Solving for P(A) = .81

To solve the question, P(B|A) = .75/.81 = .926

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