System and Component Probability Calculations

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SUMMARY

The discussion focuses on calculating system and component probabilities, specifically addressing two questions: the overall system probability and the conditional probability of a specific component's failure given the system's operation. The probability that the entire system works is established at P=0.75112. The second question regarding the probability of component A not working is deemed unanswerable due to the absence of component A in the provided diagram, leading to the conclusion that the status of component 2 is irrelevant if component 1 is not operational.

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kasse
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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...
 
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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 [tex]1[/tex]
is not working, think this way:

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

what can you do with this?
 

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