In a randomly chosen lot of 1000 bolts, let X be the number that fail to meet a length specification, and let Y be the number that fail to meet a diameter specification. Assume that the joint probability mass function of X and Y is given in the following table. y Row f(x, y) 0 1 2 totals 0 0.40 0.12 0.08 0.6 x 1 0.15 0.08 0.03 0.26 2 0.1 0.03 0.01 0.14 Column totals 0.65 0.23 0.12 1 a. Find P(X = 0 & Y = 2) b. Find P(X > 0 & Y le1) c. Find P(X 1) d. Find P(Y > 0) e. Find the probability that all bolts in the lot meet the length specification. f. Find the probability that all bolts in the lot meet the diameter specification. g. Find the probability that all bolts in the lot meet both specification.