3.36 With reference to Exercise 3.1, suppose that the points (0, 0), (0, 1), (0, 2), (0, 3), (1, 0), (1, 1), (1, 2), (1, 3), (2, 0), (2, 1), (2, 2), (2, 3), (3, 0), (3, 1), (3, 2), and (3, 3) have the probabilities 0.080, 0.032, 0.086, 0.064, 0.085, 0.073, 0.065, 0.091, 0.071, 0.050, 0.046, 0.075, 0.040, 0.021, 0.080, and 0.041.

(a) Verify that this assignment of probabilities is permissible.

(b) Find the probabilities of events A, B, and C given in part

(b) of that exercise.

(c) Calculate the probabilities that one, two, or three supplies of white cement are adulterated.