Please provide a step by step solution only for part b and be detailed. You can

Question

Please provide a step by step solution only for part b and be detailed. You can use answers from part a and c. Do note that the answer I entered for part b is wrong.

(6 points) 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. 0.080 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. 0.047 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. 0.54

Explanation / Answer

b) Probability of success, p = 1- (1 - e-x), where x = 1 year, p = 1 - (1 - e-(1/0.55)) = 0.162321
Let S denote Success and F denote Failure
There is only one way for this to happen
P(FFFFS) = 0.837680^4 * 0.162321 = 0.080

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