At the beginning of a particular work shift, a machine is in one of two states:

Question

At the beginning of a particular work shift, a machine is in one of two states: operating properly, or operating in a degraded condition. The machine is operating properly at the beginning of 90% of the work shifts, and operating in a degraded condition at the beginning of 10% of the work shifts. Given that the machine is operating properly at the beginning of the work shift, it will fail during the shift with probability 0.005. Given that the machine is operating in a degraded condition at the beginning of the work shift, it will fail during the shift with probability 0.25. What is the probability that the machine fails during the work shift?

A) 0.0045

B) 0.0250

C) 0.0295

D) 0.9205

Explanation / Answer

P(Machine Fails)

= P(Operating properly)"P(Fail | Operating properly) + P(Operating degraded)*P(Fail | Operating degraded)

= 0.90*0.005 + 0.10*0.25

= 0.0045 + 0.0250

= 0.0295

Option C is correct.

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