167 CASE STUDY United States Congress Case Study 167 Congress is made up of the House of Representatives and the Senate. Members of the House of Representatives serve two-year terms and represent a district in a state. The number of representatives for each state is determined by population. States with larger populations have more representatives than states with smaller populations. The total number of representatives is set by law at 435. Members of the Senate serve six-year terms and represent a state. Each state has 2 senators, for a total of 100 senators. The tables show the makeup of the 117th Congress by gender and political party as of January 21, 2021. The House of Representatives had 3 vacant seats. House of Representatives Political party Republican Democrat Independent Total Gender Male 182 132 0 314 Female 29 89 0 118 Total 211 221 0 432 Senate Political party Republican Democrat Independent Total Gender Male 42 32 2 76 Female 8 16 0 24 Total 50 48 2 100 EXERCISES 1. Find the probability that a randomly selected representative is female. Find the probability that a randomly selected senator is female. 2. Compare the probabilities from Exercise 1. 3. A representative is selected at random. Find the probability of each event. (a) The representative is male. (b) The representative is a Republican. (c) The representative is male given that the representative is a Republican. (d)The representative is female and a Democrat. 4. Among members of the House of Representatives, are the events “being female” and “being a Democrat” independent or dependent events? Explain. 5. A senator is selected at random. Find the probability of each event. (a) The senator is male. (b) The senator is not a Democrat. (c) The senator is female or a Republican. (d) The senator is male or a Democrat. 6. Among members of the Senate, are the events “being female” and “being an Independent” mutually exclusive? Explain. 7. Using the same row and column headings as the tables above, create a combined table for Congress. 8. A member of Congress is selected at random. Use the table from Exercise 7 to find the probability of each event. (a) The member is Independent. (b) The member is female and a Republican. (c) The member is male or a Democrat.
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