Question

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 pulations. The total number of representatives is set by law at 435. Members of nate serve six-year terms and represent a state. Each state has 2 senators, total of 100 senators. The tables show the makeup of the 115th Congress by genderandpolitical party as of January 3,2017 Honse of Representatives Political party DemocratIndependentTotal Male GenderFemale23 Total 21 129 347 241 435 Senate Political party RepublicanDemocrat IndependentT Male 47 30 16 46 79 21 100 Gender Female Total 52 EXERCISES 1. Find the probability that a randomly selected 5. A senator s selected at random. Find the representative is female. Find the probability 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. that a randomly selected senator is female. 2. Compare the probabilities from Exercise 1. 3. A representative is selccted at random. Find tho probability of each event. (a) The representative is male. (b) The representative is a Republican. (c) The representative is male given that the 6. Among members of the Senate, are the events "being female" and "being an Independent mutually exclusive? Explain. representative is a Republican. 7. Using the same row and column headings as (d) The representative is female and a Democrat the tables above, create a combined table for Congress. 4. Among members of the House of 8. A member of Congress is selected at random. Representatives, are the events "being female" and "being a Democrat" independent or dependent events? Explain. Usc the table from Exercisc 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.

Answer 1

1.
Probability that a representative is female = 88/435 = 0.2023
Probability that a senator is female = 21 / 100 = 0.21

2.
The probability that a representative is female is approximately same as probability that a senator is female.

3.
(a)
Probability that a representative is male = 347/435 = 0.7977
(b)
Probability that a representative is Republican = 241/ 435 = 0.554
(c)
P(male | Republican) = P(male and Republican) / P(Republican) = 218/241 = 0.9046
(d)
Probability that a representative is female and Democrat = 65/435 = 0.1494

4.
From 3 (d), P(Female and Democrat) = 0.1494
P(Female) = 88/435 = 0.2023
P(Democrat) = 194 / 435 = 0.446
P(Female) * P(Democrat) = 0.2023 * 0.446 = 0.0902

As, P(Female) * P(Democrat) is not equal to P(Female and Democrat), the events "being female" and "being Democrat" are not independent and hence are dependent events.