A fluid flow system connecting points X and Y is illustrated schematically below

Question

A fluid flow system connecting points X and Y is illustrated schematically below. Fluid can only flow through each labeled junction when that "switch" is closed. Each switch is independent of the others, and the probability that any given switch is open is 80%. What is the probability that fluid flows from X to Y? What is the probability that fluid flows from X to Y, given that switch D is open? Suppose switch E always copies the status of switch A. What is the probability that fluid flows from X to Y?

Explanation / Answer

a. The fluid can flow from X to Y , provided any of the following states

> A,C,D are closed

> A,C,E are closed

> B,C,D are closed

>B,C,E are closed

Thus reqd probability = 4*0.2*0.2*0.2 = 0.032

B. Given D is open, thus possible cases areB,C,E closed or A,C,E closed

Thus probability =2*0.2*0.2*0.2 =0.016

C. If both E and A are closed, then the required probability =0.2*0.2*0.2 =0.008

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