Suppose the diagram of an electrical system is as given in Figure 2.10. What is the probability that the system works? Assume the components fail independently
I got the answer for the probability of all the system works and it is $0.8037$ but there is another question.
Given that the system works, compute the probability that component B is working.
I am not sure about this one. But is the calculation like this? $$ P(A \cup B \cup C \cup D)/0.8037 $$ or
only $P(A \cup B \cup D)/0.8037$ since we are only talking about B is working given that the system works.