Problem 44315. Predicting life and death of a memory-less light bulb

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You have a light bulb that can fail any moment according to the exponential probability distribution.

At any moment, the probability that it will survive just N hours = exp(-N*P), where P is a constant.

Notice that this probability is very small if N is very large.

Now suppose, the bulb has already survived N hours.

Please calculate the probability of its surviving M more hours.