A homeowner wants to purchase multiple electric pumps and operate them in parallel to ensure that she can handle any basement flooding that occurs. A single electric pump is enough to handle any 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 is the required minimum reliability of each pump?

(b) Now suppose the manufacturer specifies each electric pump has a 0.75 reliability. How many would need to be purchased?

(c) After some searching, another more reliable gas-powered pump with the same output capacity as the electric pump was found. These gas-powered pumps have a reliability of 0.85 but cost $1000 dollars each. The electric pumps cost $600. If she is going to buy only one type of pump, what is the cheapest option to meet her reliability goal? What if she is willing to buy both kinds of pumps?