help plz with these two problems Name Problem 1. A city has two sources of water
ID: 3128903 • Letter: H
Question
help plz with these two problems
Name Problem 1. A city has two sources of water available t sufficient to supply the water needs of the city. it is then pumped to the city through a single pipe. A disruption. Pipe 1 has a 99.5% chance of uninterrupted a 99.9% chance of uninterrupted flow. es of wat er available to it- Source A and Source B. Either source alone is of the city. Water from eitl city. Water from either source is pumped to a junction where flow; pipe chance of as a 99.5%ingle pipe. Any of the three pipes could experience a flow uninterrupted flow. or uninterrupted flow; pipe 2 has a 99% chance; and pipe 3 has Source A A) Wh 1 junction at is the probability that the junction will experience a decrease in flow due to an upstream interruption in one of the pipes? 2 B) What is the p t is the probability that the city will experience Source B an interruption of their water supplyExplanation / Answer
Let A shows the event that pipe 1 has uninterrupted flow, B shows the event that pipe 2 has uninterrupted flow and C shows the event that pipe 3 has uninterrupted flow. So we have
P(A) = 0.995, P(B) = 0.99, P(C) = 0.999
(a)
Junction will experienced decresed flow if one the pipe is not working but other is working. Since pipes are independent so the probabaility junction experince in decrease in flow will be
P(Junction experienced decrease in flow) = P(pipe 1 working but not pipe 2) +P(pipe 2 working but not pipe 1)
=P(A)[1-P(B)]+P(B)[1-P(A)] = 0.995 (1-0.99) + (1-0.995) (0.99) = 0.00995 + 0.00495 = 0.0149
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(B)
City will feel inetrruption ethier both pipe 1 and pipe 2 are not working or pipe 3 is not working so the required probabaility is
[1-P(A)]*[1-P(B)] + [1-P(C) ] = [1-0.995][1-0.99] + [1-0.999] = 0.00005 + 0.001 = 0.00105
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