Question 5

Scenario: A boiler has four identical relief valves. Assume independent operation of the valves.

Events:

  • - A valve opens on demand.

Probabilities:

  • .

(a)

Problem: Calculate .

Process: The probability that at least one valve opens is equivalent to the probability of the complement that no valve opens.

Answer: 0.99999744.

(b)

Problem: Calculate .

Process: The probability that at least one valve fails to open is equivalent to the probability of the complement that all valves open.

Answer: 0.1507.