Salespersons Adams and Jones call on three and four customers, respectively, on a given day.

Adams could make 0, 1, 2, or 3 sales, whereas Jones could make 0, 1, 2, 3, or 4 sales. The sample space listing the number of possible sales for each person on a given day is shown in the table. (3, 1 stands for 3 sales by Jones and 1 sale by Adams.)

Jones Adams 0 1 2 3 4 0 0, 0 1, 0 2, 0 3, 0 4, 0 1 0, 1 1, 1 2, 1 3, 1 4, 1 2 0, 2 1, 2 2, 2 3, 2 4, 2 3 0, 3 1, 3 2, 3 3, 3 4, 3 Assume that each sample point is equally likely.

Consider these events:

A: At least one of the salespersons made no sales.

B: Together they made exactly three sales.

C: Each made the same number of sales.

D: Adams made exactly one sale.

Find the probabilities by counting sample points:

a. P(A)

b. P(B)

c. P(C)

d. P(D)

e. P(A and B)

f. P(B and C)

g. P(A or B) h. P(B or C) i. P(A  B)

j. P(B  D) k. P(C  B) l. P(B  A)

m. P(C  A) n. P(A or B or C)

Are the following pairs of events mutually exclusive?

Explain.

o. A and B p. B and C q. B and D Are the following pairs of events independent? Explain.

r. A and B s. B and C t. B and D