The life times, Y in years of a certain brand of low-grade lightbulbs follow an exponential distribution with a mean of 0.55 years. A tester makes random observations of the life times of this particular brand of lightbulbs and records them one by one as either a success if the life time exceeds 1 year, or as a failure otherwise.
Part a) Find the probability to 3 decimal places that the first success occurs in the fifth observation.
Part b) Find the probability to 3 decimal places of the second success occurring in the 8th observation given that the first success occurred in the 3rd observation.
Part c) Find the probability to 2 decimal places that the first success occurs in an odd-numbered observation. That is, the first success occurs in the 1st or 3rd or 5th or 7th (and so on) observation.