10. The lifetime (in hours) of a light bulb manufactured by a certain company is a random variable with probability density function

Suppose that, for all nonnegative real numbers a and

b, the event that any light bulb lasts at least a hours is independent of the event that any other light bulb lasts at least b hours.
Find the probability that, of six such light bulbs selected at random, exactly two last over 1000 hours.

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0 f(x) = 5 x 105 2:3 if x 500 if x > 500.