Superlesson
Project 11-1
Advanced Algebra
Chapter 11, Advanced Techniques for Chance and Data
In the following investigations, you'll use data to calculate probabilities relating to U.S. governors, U.S. senators, and voting patterns in the 1996 Presidential election.
Part B, The Probability of A or B
1. Use data on U.S. governors found at the Governor Web site. to find the probability that a randomly chosen state governor meets the given conditions. (Note: The list includes five non-state governors, the governors of American Samoa, Guam, Northern Mariana Islands, Puerto Rico, and the Virgin Islands.)
a. The governor is a Republican.
b. The governor is not a Democrat.
c. The governor is the governor of your state.
d. The governor served at least one previous term.
e. The governor is a woman. Use data from the Women Governors Web site to answer this question.
f. The governor is a woman or is serving a regular term of 2 years.
g. The governor is a lawyer or an Independent. Use data from the Search Governors Web site to answer this question. (Note that the list of lawyers includes the governor of American Samoa.)
h. Use data on U.S. governors to give an example of an event and the complement of the event. Show that the sum of the probabilities of the events equals 1.
Part B, Independent and Dependent
Events
2. Use the Internet to answer the questions below.
a. What is the probability that a randomly chosen U.S. voter who turned out for the 1996 Presidential election was from Connecticut? Use the data from the Voter Registration Web site to answer this question.
b. What is the probability that a randomly chosen voter in the 1996 election voted for Green Party candidate Ralph Nader? Use the data from the Popular Vote Web site to answer this question.
c. Based on your answers to a and b, what is the probability that a randomly chosen voter in the 1996 election was from Connecticut and voted for Ralph Nader?
d. Based on the actual Connecticut vote, what is the probability that a randomly chosen voter in the 1996 election was from Connecticut and voted for Ralph Nader? Refer to the Presidential Election Results Web site.
e. What conclusion can you draw from these results?
Part C, Conditional Probability
3. Using the Internet, answer the following questions.
a. What is the probability that a randomly chosen U.S. Senator whose term expires in 2001 is a Democrat? Use the data from the Class Membership Web site to answer this question.
b. What is the probability that a randomly chosen senator from Ohio is a Republican? Use the data from the Directory of Senators by State Web site to answer this question.
c. What is the probability that a randomly chosen senator is a Democrat who serves on the Committee on Agriculture, Nutrition and Forestry? Use the data from the Committe and Subcommitte Membership Web site to answer this question.
d. What percent of the senators in the above group (3c) are from South Dakota?
e. Show how you can use your answers to (3c) and (3d) to find the probability that a randomly chosen senator is a South Dakota Democrat who serves on the Committee on Agriculture, Nutrition and Forestry.