System and Component Probability Calculations

[kasse]

The numbers represent the probability that each component works.

a) What's the probability that the entire system works?
b) Given that the system works, what's the probability that the component A is not working?

a) P=.75112, easy
b) Don't know what to do here...

 

[statdad]

Since there is no component A in the diagram, I'd say you can't answer the second question.
If you were asking this: Given the system works, what is the probability $$1$$
is not working, think this way:

If the system is operating, you know that
* $$3, 4$$ and $$5$$ are all operating
and
* $$1$$ is not operating, status of $$2$$ is unimportant

what can you do with this?