The four staff members, A, B, C, and D, of a college drama department use the weighted voting system {8: 5, 4, 3, 2} to make casting decisions for a play they are producing. In this voting system, voter A has a weight of 5, voter B has a weight of 4, voter C has a weight of 3, and voter D has a weight of 2. Compute the Banzhaf power index for each member of the department.
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The four staff members, A, B, C, and D, of a college drama department use the weighted voting system {8: 5, 4, 3, 2} to make casting decisions for a play they are producing. In this voting system, voter A has a weight of 5, voter B has a weight of 4, voter C has a weight of 3, and voter D has a weight of 2. Compute the Banzhaf power index for each member of the department.
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- A researcher surveys 200 randomly selected college students to determine the number of education majors and mathematics majors. 16% of the students surveyed are education majors and 6% of the students surveyed are mathematics majors. 2% of the students are both education majors and mathematics majors. What percentage of the students surveyed are education majors or mathematics majors?The students in a class get to decide on the color of the classroom. The two choices are blue and yellow. Polling shows yellow is preferred by a small majority, 53% for yellow to 47% for blue. However, before the vote is held, a new color choice is added: red. Not a lot of people like red, but there are some yellow supporters who would actually vote for red. The results of the vote are below. Blue Yellow Red 46% 44% 10% What statement below is correct about adding a third choice to the plurality vote? O a Ob Oc d Red did not win the vote, but it draws enough support away from yellow to make blue the winner, even though a majority of students preferred yellow over blue when there were two choices. Red did not win the vote, but it had no effect on drawing enough support away from yellow to make blue the winner, even though a majority of students preferred yellow over blue when there were two choices. Red did not win the vote, so because of this, yellow should win the vote over blue.…At the beginning of each football season, the coaching staff at Vista High School must vote to decide which players to select for the team. They use the weighted voting system {7: 6, 5, 1}. In this voting system, the head coach A has a weight of 6, the assistant coach B has a weight of 5, and the junior varsity coach C has a weight of 1. Compute the Banzhaf power index for each of the coaches. (Round your answers to the nearest hundredth.) BPI(A) = BPI(B) = BPI(C) =
- At the beginning of each football season, the coaching staff at Vista High School must vote to decide which players to select for the team. They use the weighted voting system {4: 3, 2, 1}. In this voting system, the head coach A has a weight of 3, the assistant coach B has a weight of 2, and the junior varsity coach C has a weight of 1. The head coach has decided that next year the coaching staff should use the weighted voting system (10: 9, 8, 1}. The head coach is still voter A, the assistant coach is still voter B, and the junior varsity coach is still voter C. (a) Compute the Banzhaf power index for each coach under this new system. (Round your answers to the nearest hundredth.) BPI(A) BPI(B) BPI(C) (b) How do the Banzhaf power indices for this new voting system compare with the first Banzhaf power indices? Measured by the BPI, the head coach gained power. Measured by the BPI, the assistant coach gained power. O Measured by the BPI, the junior varsity coach lost power. O The BPI…Bob is a recent graduate of Industrial Engineering. During his job search, Bob compiled information about the top 300 multinational companies with offices in Toronto; and which of these companies also had offices in San Francisco, New York, and London. Here are the results of Bob’s research: 20% of the companies have offices only in London. 40 companies have offices only in San Francisco. 50 companies have offices in the 3 cities. 115 companies have offices in New York. 15% of the companies have offices in London and one other city. 10 companies have offices in San Francisco and New York, but do not have an office in London. 20 companies have offices in New York and London, but do not have an office in San Francisco. What is the probability that the company has offices in exactly two of the (non-Toronto) cities ?Bob is a recent graduate of Industrial Engineering. During his job search, Bob compiled information about the top 300 multinational companies with offices in Toronto; and which of these companies also had offices in San Francisco, New York, and London. Here are the results of Bob’s research: 20% of the companies have offices only in London. 40 companies have offices only in San Francisco. 50 companies have offices in the 3 cities. 115 companies have offices in New York. 15% of the companies have offices in London and one other city. 10 companies have offices in San Francisco and New York, but do not have an office in London. 20 companies have offices in New York and London, but do not have an office in San Francisco.(a) Draw the Venn diagram that represents this situation
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- The class field trip to the zoo was a huge success! The kids especially liked the bears, the dolphins, the monkeys, and the elephants. Taking a poll, the teachers found the following: all those who liked bears also liked the monkeys. Half of those who liked dolphins also liked monkeys. There were 24 who liked dolphins. However, none of those who liked elephants also liked bears. There were 16 who liked dolphins but not elephants. All those who liked elephants also liked monkeys. Half of those who liked elephants also liked dolphins. None who liked bears also liked dolphins. There were 9 who liked only monkeys. There were 15 who liked bears. How many liked monkeys? How many liked monkeys, elephants, and dolphins – all 3?You know that 70 percent of the subs at theme parks in the US are yellow. There are 220 subs in theme parks in the US. You are in a contest where you select sub names from a hat and record the name of the theme park sub. ( No replacement ). You win a prize if you select a greater percentage of yellow subs than 90% of your many many competitors. What percentage of yellow subs do you need to select if you select 50 subs? ( Hint : Use the finite population correction factor ).