13. A law firm is run by four partners (A, B, C, and D). Each partner has one vote, and decisions are made by a majority rule, but in the case of a 2-2 tie the coalition with a senior partner wins. a) List all of the winning coalitions in this voting system and critical players in each. Indicate all losing coalitions by typing Lose into the answer space. For the remaining winning coalitions, type in the critical player(s) in each coalition in ascending order, separated by commas but no spaces (ex. P5,P6). If there are no critical players, type n/a. (A} KA, B} КА, В, С} КА, В, С, D} {B} KA. C} {A, B, D} (C} KA, D} (A, C,D} {D} {B, C} (В, С, D} (B,D} {C,D} b) Find the Banzhaf power index of this law firm. Type your answers as percentages rounded to two decimal places, no percentage sign (ex. 50.00). B1

Determines who wins the plurality vote and who wins the rank voting or preferential voting method in the election. 1. There are 650 students in a school, and they all get to vote for the school president. There are 3 candidates: Rios, • Millie, • Charles. Each student will receive a ballot and they will rank the candidates in or of 1", 2nd, and 3rd choice. Remember on the preferential vote the winning candidate must have 1 more than half the votes. See the results of the election below. Votes 225 175 250 225 1¹ Millie Charles Rios 250 and a. The person who has the largest number of first place votes is b. The person who has the fewest number of first place votes is c. The candidate we eliminate is d. Fill in the new table. 1 Charles Millie Millie Rios Rios Charles 2rd Is there a majority of votes for a candidate now? If yes, who is that candidate, and how many the first place votes does that candidate have? f. Who won the plurality vote or single candidate voting method? Explain how…

A standard deck of cards has 52 cards in four suits: spades, hearts, diamonds, and clubs. Spades and clubs are black; hearts and diamonds are red. Each suit has 13 cards: 2 through 10, Jack, Queen, King, Ace. The "face cards" are the Jack, Queen, and King. Robby Billity shuffles a standard deck and draws one card. Then Robby Replaces the card, shuffles again, and draws another card. He repeats this procedure for a total of 1000 draws. About how many times would we expect Robby to draw these cards?  A) the ace of spades B) a face card in any suit

The board of directors of a pharmaceutical corporation has 10 members. An upcoming stockholders' meeting is scheduled to approve a new slate of company officers (chosen from the 10 board members) How many different slates consisting of a president, vice president, secretary, and treasurer can the board present to the stockholders for their approval?

Hale Middle School is going to select a committee. The committee will have a faculty member, a male student, a female student, and a parent. Here are the positions and the people interested in each. Position People interested Faculty member Mrs. Gray, Ms. Foster, Mr. Harris Male student Female student Abdul, Ravi, Sam, Chris Laura, Christine, Melissa, Karen Dr. Peterson, Mr. Hughes, Ms. Clark, Ms. Hernandez Based on this list, how many ways are there to fill the four committee positions? Parent Explanation Check X 5 hp Ⓒ2022 McGraw Hill LLC. All Rights Reserved Terms of Use Privacy Ce

2. Let A 3 {0, 1, а, b, 8, 10, с, — 4}, В %3 {3, 1,9, е, а, с, 0}, and C 3D {2, с, 10, 9, 8, — 4, 11, е, 3, 0}. Find AПВ, AUB, А-С, Вnc

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