Question

Company ABC has one thermostat, two boilers, and one water gauge. For a company to be properly heated, the thermostat and a minimum of one boiler must be operational (both boilers can also be operational). The water gauge is not a factor. History shows that each boiler is operational 72% of the time. The thermostat is operational 94% of the time and the water gauge is operational 87% of the time. Failures of either the thermostat, boilers or water gauge are independent of each other. What is the probability that company ABC is properly heated.

Answer 1

Let T shows the event that thermostat is operational and B shows the event that at least one boiler is opeartional. The probability that thermostat is operational is

P(T) = 0.94

The probability that both boiler is not operational is (1 - 0.72)*(1-0.72) = 0.0784

By the complement rule, the probability that at least one boiler is oprational is

P(B) = 1 - 0.0784 = 0.9216

Since water guage is not a factor so the probability that company ABC is properly heated is

P(T) * P(B) = 0.94 * 0.9216 = 0.866304

Answer: 0.8663