A homeowner wants to purchase multiple electric pumps and operate them in parallel to ensure that...

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A homeowner wants to purchase multiple electric pumps andoperate them in parallel to ensure that she can handle any basementflooding that occurs. A single electric pump is enough to handleany flooding, but the pumps are not very reliable. She wants to be%99.99 sure that there will be a working pump during a flood.
(a) If she only wants to buy 3 identical electric pumps, what isthe required minimum reliability of each pump?
(b) Now suppose the manufacturer specifies each electric pumphas a 0.75 reliability. How many would need to be purchased?
(c) After some searching, another more reliable gas-powered pumpwith the same output capacity as the electric pump was found. Thesegas-powered pumps have a reliability of 0.85 but cost $1000 dollarseach. The electric pumps cost $600. If she is going to buy only onetype of pump, what is the cheapest option to meet her reliabilitygoal? What if she is willing to buy both kinds of pumps?

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3.6 Ratings (260 Votes)

The reliability that needs to be achieved here is 9999 sure that atleast one of pumps work This means we need to buy as many pumps such that the probability that none of the pumps work is less than 00001 which is 109999 Since each pump working or See Answer

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