You've been asked to evaluate the lighting system for a stairway that serves as an emergency exit path. This stairway has a lighting fixture that holds three light bulbs. Three different bulb types have been installed in the fixture: Bulb Type A is an incandescent device that emits 1000 lumens. Its probability of failure increases linearly over time according to the equation: P(failure) = 0.02 x t where t is the number of months since the bulb was installed. Bulb Type B is a compact fluorescent device that emits 800 lumens. Its probability of failure increases linearly over time according to the equation: P(failure) = 0.005 x t where t is the number of months since the bulb was installed. Bulb Type C is a LED device that emits 500 lumens. Its probability of failure increases linearly over time according to the equation: P(failure) = 0.001 x t where t is the number of months since the bulb was installed. Note--The lighting fixture is powered by the electric grid and there is no battery backup. Records provided by the electric utility indicate that the electric grid functions properly 99.2 percent of the time. 1. Part 1--Assume that all three light bulbs are replaced at the same time (t =0). What is the probability of having a completely dark stairwell 8 months after the bulbs have been replaced