A manufacturer determines that a big screen HDTV set had probabilities of \(0.8,0.15,0.05\), respectively, of being placed in the categories acceptable, minor defect, or major defect. If 3 HDTVs are inspected,

(a) find the probability that 2 are acceptable and 1 is a minor defect;

(b) find the marginal distribution of the number in minor defect;

(c) compare your answer in part

(b) with the binomial probabilities \(b(x ; 3,0.15)\). Comment.