A group of fun-loving people have decided to play a practical joke on one of their friends, but they can't decide which friend, Alice (A), Betty (B), or Connie (C). Their preferences are: (ABC) (CBA) (BCA) 1,3, 4Who wins using the Borda count method?
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- The following are the rules of the game: One player is chosen to be the "It" that guards the preso (empty can). The rest of the players are the hitters, and each throws the pamato (slipper) to the toe-line to topple down the preso. If a player throws the farthest from the toe-line, he/she becomes the "It". The hitters are divided between the two opposite sides. When the hitters run out of throwing objects, the game translates into a chase. Players on one side will act as bait while those on the other side will try to kick the can to avoid being tagged. R2: R3: R4: R5: R6: Given the set of rules of the game, answer the following: 1. Identify the simple statements, compound statements, and the connectives involved in compound statements. Explain your answer. 2. Make a twist in the game by adding a new rule to the game or replacing one of the rules of the game.If P(A) = 0.6 and P(B) = 0.25, and P(A and B) = 0.3, determine P(A or B)Now suppose you have a box of cookies. Inside the box you have: 18 Chocolate Cookies (8 Circle-shaped, 6 Heart-shaped, 4 Bear-shaped) 15 Vanilla Cookies (4 Circle-shaped, 8 Heart-shaped, 3 Bear-shaped) Suppose you draw one cookie from the box at random: (c) P(Cookie is Heart-shaped) =(d) P(Cookie is Chocolate AND Bear-shaped) =(e) P(Cookie is Vanilla OR Circle-shaped) = (f) P(Cookie is Chocolate | Cookie is Bear-shaped) =(g) P(Cookie is Heart-Shaped | Cookie is Vanilla) = Now suppose you draw two cookies from the box at random without replacement. (h) P(Both Cookies are Chocolate) =
- A group of fun-loving people have decided to play a practical joke on one of their friends, but they can't decide which friend, Alice (A), Betty (B), or Connie (C). Their preferences are: (ABC) (CBA) (BCA) 6 10 9 Who wins using the Borda count method? Does this violate the Condorcet criterion?A group of fun-loving people have decided to play a practical joke on one of their friends, but they can't decide which friend, Alice (A), Betty (B), or Connie (C). Their preferences are: (CAB) (BAC) (ABC) 7 ,6 ,5 Who wins the election using the Hare method? If P(A)=.5, P(B)= .5, and P(A and B)= .47, find P(A or B)
- A technology store holds a contest to attract shoppers. works: An ace and four other cards are shuffled and placed face down on a table. The customer gets to turn over cards one at a time, looking for the ace. The person wins $100 of store credit if the ace is the first card, $50 if it is the second card, and $20, $10, or $5 if it is the third, fourth, or last card chosen. What is the average dollar amount of store credit given away in the contest? Estimate with a simulation of 10 trials. Once an hour, someone at checkout is chosen at random to play in the contest Here's how it 67819 00354 91439 91073 49258 15992 41277 75111 67496 68430 09875 08990 27656 15871 23637 00952 97818 64234 50199 05715Sam bought 9 tickets all in the same row to a KC Royals game for himself and his friends next week. His friends are Eric, Sarah, Renee, David, Julie, Derek, Kelsey and kyle. (a) How many different ways can the friends be seated in the row?(b) Sam has a crush on Sarah, so he wants to make sure his seat is next to hers. How many ways are there to assign the seats now?(c) How many ways are there to assign the seats if Sam wants to ensure that they are all seated boy-girl-boy-girl?A bag of marbles had 27 green marbles and the rest were yellow. For a game, 30 marbles were chosen from the bag. Of these 30 marbles chosen, green. Use this information to answer the questions below. If not enough information is given to answer a question, click on "Not enough information." (a) How many of the bag's marbles were not chosen? (b) How many of the bag's green marbles were chosen? (c) How many of the bag's green marbles were not chosen? 0 0 Hot h X 7 10 were
- At the National Baseball Batting Contest, the organizers have set up game booths for the contestants. Richard wants to win a large stuffed animal. The rules of the game are as follows: You are pitched 5 fastballs, and you must hit them into a fair zone to count. • If you successfully hit all 5 pitches, you win a large stuffed animal. If you successfully hit 3 or 4 pitches, you win a small stuffed animal. • If you successfully hit 1 or 2 pitches, you win a bat-shaped pencil. If you miss all the pitches, you do not win a prize. • The game costs $3 to play (each set of 5 fastballs). Everyone has the same chance as Richard to win. If 160 people each play the game once, how many large stuffed animals will be won?Given P(A) = 0.47, P(B) = 0.34, P(A or B) = 0.36, what is P(A and B)?The most popular game at the Whoville Resort and Casino (WRC) is "Pick Green", which is played with the WRC's Great Urn of Joy. This urn contains thousands of marbles: 85% red and 15% green. The game costs $1 to play and the rules simple: After paying $1, the player repeatedly draws one marble at random, with replacement from the Great Urn of Joy, until they draw a red marble. The player then receives a payoff based on the number of green marbles that they drew, according to the following table: #green marbles 0 1 2 3 4 or more payoff SO $1 $5 $100 $1000 While it is true that Whos don't earn extra cash for drawing more than 4 green marbles, they do get a certificate listing their total, and these certificates are a source of great pride in Whoville. What is the probability that a player receives (exactly) $5 in this game? What is the probability that a player receives at least $1 in this game? Consider the WRC's point of view: their profit-per-game is $1 - payoff. What is the expected…