Joe just replaced two lightbulbs one of which is rated 60 watts with an exponentially distributed lifetime whose mean is 200 hours, and the other is rated 100 watts with an exponentially distributed lifetime whose mean is 100 hours.
a. What is the probability that the 60-watt bulb fails before the 100-watt bulb?
b. What is the mean time until the first of the two bulbs fails?
c. Given that the 60-watt bulb has not failed after 300 hours, what is the probability that it will last at least another 100 hours?