For all problems where you are asked to show or explain your work, you may use your calculator, as long as you explain how you did it in the calculator.
Post the following in DF Module 2 Activity. I hope that you will take a look at your classmates posts after you are done to compare your results.
115th United States Congress
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 each state has 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. Members of the Senate serve six-year terms and represent a state. Each state has 2 senators, for a total of 100. The tables show the makeup of the 115th Congress by gender and political party. There is one vacant seat in the House of Representatives.
|Political party vs Gender in House of Representatives|
|Political party vs Gender in the Senate|
Post 1 (Your original post)
Find the following probabilities. Leave your answers in fraction form or round to the nearest thousandth.
- Find both probabilities:
- Find the probability that a randomly selected representative is female.
- Find the probability that a randomly selected senator is female.
- Compare the probabilities from Exercise 1.
- A representative is selected at random. Find the probability of each event.
- The representative is male.
- The representative is a Republican.
- The representative is male given that the representative is a Republican.
- The representative is female and a Democrat.
- Are the events “being female” and “being a Democrat” independent or dependent events? Explain. You will need to use the definition on page 148.
- A senator is selected at random. Find the probability of each event.
- The senator is male.
- The senator is not a Democrat.
- The senator is female or a Republican.
- The senator is male or a Democrat.
- Are the events “being female” and “being an Independent” mutually exclusive? Explain.
- Using the same row and column headings as the tables above, create a combined table for Congress:
|Political party vs Gender in the Congress|
- A member of Congress is selected at random. Use the table from Exercise 5 to find the probability of each event.
- The member is Independent.
- The member is female and a Republican.
- The member is male or a Democrat.
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