3.63 Given that P (A) = 0.60, P (B) = 0.40, and P (A∩B) = 0.24, verify that

(a) P(A | B) = P(A);

(b) P(A | B ) = P(A);

(c) P(B | A) = P(B);

(d) P(B | A ) = P(B). 3.64 Among 40 condensers produced by a machine, 6 are defective. If we randomly check 5 condensers, what are the probabilities that

(a) none are defective;

(b) all are defective? 3.65 Among 50 students enrolled in a college, 40 had applied for civil engineering and 10 had applied for mechanical engineering. If two students have been enrolled in software engineering by mistake, and the “selection” is random, what are the probabilities that

(a) both had applied for civil engineering;

(b) both had applied for mechanical engineering;

(c) one had applied for civil engineering and one had applied for mechanical engineering?