11 The lifetime (in hours) of a lightbulb manufactured by a certain company is a random variable with probability density function 0 f(x) = 5 x 10 if x 500 if x > 500. Suppose that, for all nonnegative real numbers a and

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