The timetofailure in months X of light bulbs produced at two

The time-to-failure in months, X, of light bulbs produced at two manufacturing plants A and B obey, respectively, the following CDFs F_X (x) = (1 - e ) u(x) for plant A F_X (x) = (1 - e ) u(x) for plant B. Plant B produces three times as many bulbs as many bulbs as plant A. The bulbs, indistinguishable to the eye, are intermingled and sold. What is the probability that a bulb purchased at random will burn at least two months; five months; seven months?

Solution