At the beginning of a particular work shift, a machine is in one of three states: operating properly, operating in a minor degraded condition, or operating in a major degraded condition. The machine is operating properly at the beginning of 70% of the work shifts, and operating in a minor degraded condition at the beginning of 22% 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 minor degraded condition at the beginning of the work shift, it will fail during the shift with probability 0.18. Given that the machine is operating in a major degraded condition at the beginning of the work shift, it will fail during the shift with probability 0.45.
What is the probability that the machine fails during the work shift?