U.S. Congress. The U.S. Congress, Joint Committee on Printing, provides information on the composition of Congress in Congressional Directory. Here is a joint probability distribution for the members of the 113th Congress by legislative group and political party. The “other” category includes Independents and vacancies.

(Rep = Representative.) Party Group Rep Senator C1 C2 P(Pi)

Democratic 0.374 0.097 0.471 P1 Republican 0.434 0.086 0.520 P2 Other 0.006 0.004 0.009 P3 P(Cj) 0.813 0.187 1.000

a. Determine P(P1), P(C2), and P(P1 & C2).

b. Use the special multiplication rule to determine whether events P1 and C2 are independent.