2. Two pumps connected in parallel fail independently of one another on any give

Question

2. Two pumps connected in parallel fail independently of one another on any given day. The probability that only the older pump will fail is 0.10, and the probability that only the newer pump will fail is 0.05. (a) What is the probability that the older pump will fail and the newer pump operate on any given day? (b) What is the probability that both the older pump and the newer pump operate on any given day? (c) What is the probability that the pumping system will operate on any given day?

3. A boiler has three identical relief valves. The probability that any particular valve will open on demand is 0.8. Assuming independent operation of the valves, calculate each of the following probabilities when the boiler operates and valves are on demand, (a) P(no valve opens); (b) P(exactly one valve opens); (c) P(at least one valve opens); (d) P(at least one valve fails to open); (e) P(exactly two valves open).

Explanation / Answer

A: only the older pump will fail

B: only the newer pump will fail

P(A)=0.1

P(B)=0.05

a) P(A and not B)=P(A)*P(not B)=0.1*(1-0.05)=0.095

b) P(not A and not B)=(1-0.1)*(1-0.05)=0.855

c) 1-P(A and B)=1-p(A)*p(B)=1-0.1*0.05 =0.995

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