Probability that the right headlight

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Reference no: EM13822851

I recently had to replace both front headlights on my car. The life expectancy of my headlights follows an exponential distribution with a MTBF of 1500 hours. That is, the expected number of hours until failure is 1500 hours. For the purposes of this problem assume that both headlights were initially installed at the same time, are identical models and are always on at the same time.

What is the probability that the right headlight will burn out in 950 hours or less of operation?
What is the probability that both headlights burn out in 950 hours or less of operation?
Sure enough the right headlight burns out at the 950th hour of operation. Now suppose that I get the right headlight replaced. As I am driving some time later, I nervously await the right headlight failing after 950 hours but nothing happened. I start feeling lucky and believe that the right headlight will last at least another 950 hours. What is the probability that my right headlight will last for at least 1900 hours given that it has not failed after 950 hours?

Reference no: EM13822851

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