. A boiler has five identical relief valves. The probability that any particular valve will open on demand is .95. Assuming independent operation of the valves, calculate P(at least one valve opens)...

. A boiler has five identical relief valves. The probability that any particular valve will open on

demand is .95. Assuming independent operation of the valves, calculate P(at least one valve

opens) and P(at least one valve fails to open).

. Two pumps connected in parallel fail independently of each other on any given day. The

probability that only the older pump will fail is. 10, and the probability that only the newer

pump will fail is .05. What is the probability that the pumping system will fail on any given day

(which happens if both pumps fail)?