Ages of Senators. According to the Congressional Directory, the official directory of the U.S. Congress, prepared by the Joint Committee on Printing, the age distribution for senators in the U.S. Congress as of Fall 2013, is as shown in the following table.

Age (yr) No. of senators Under 50 11 50–59 30 60–69 37 70–79 20 80 and over 2 Suppose that a U.S. senator is selected at random. Let A = event the senator is under 50, B = event the senator is in his or her 50s, C = event the senator is in his or her 60s, and S = event the senator is under 70.

a. Use the table and the f/N rule to find P(S).

b. Express event S in terms of events A, B, and C.

c. Determine P(A), P(B), and P(C).

d. Compute P(S), using the special addition rule and your answers from parts

(b) and (c). Compare your answer with that in part (a).