In: Statistics and Probability
When commercial aircraft are inspected, wing cracks are reported as nonexistent, detectable, or critical. The history of a particular fleet indicates that 70% of the planes inspected have no wing cracks, 25% have detectable wing cracks, and 5% have critical wing cracks. Five planes are randomly selected.
(a) Find the probability that one has a critical crack, two have detectable cracks, and two have no cracks.
(b) Find the probability that at least one plane has critical cracks.
(c) Find the variance of number of planes having cracks (detectable and critical).