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Probability - system of components

Folks,

I am trying to get a validation on the following probability question, I have worked out the answer (I think). There is an attachment which details the network diagram. Thanks in advance.

For the system below each circular component shown fails with probability 0.10. Each rectangular component shown fails with probability 0.20. The system as a whole functions correctly if and only if it is possible to trace a path of functioning components from A to B. Calculate the probability of the system functioning (assuming all the components are independent).