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- On an 18-hole golf course, there are par-3 holds, par-4 holes, and par-5 holes. A golfer who shoots par on every hole has a score of 72. The course designers want there to be the same number of par-3 holes as there are par-5 holes. What are the different combinations of each type of hole on the golf course could there be?Traditionally, the game of Rock, Paper, Scissors is played with two people. Each of the two people, on the count of 3, reveals their hand in the shape of a rock, a piece of paper, or a pair of scissors as best they can (usually with a closed fist, a flat hand, or their index and middle fingers outstretched to form the V of an open pair of scissors). As the rules go, rock smashes scissors, paper covers rock, and scissors cuts paper. The game can be extended to an arbitrarily large number of, say, nn people, where nn is greater than or equal to 2. If when all nn people reveal their play and only 1 or all 3 options appear, that round is deemed indecisiveindecisive and they just play again. If when all nn people reveal their play precisely two of the three options appear, that round is decisivedecisive, and those with the winning play continue while those with the losing play are eliminated. Play continues until only one person remains. Assume the game begins with nn players, each of whom…You and two friends decide to go to a casino and play Blackjack. You find an empty table and sit down. The dealer shuffles and deals from a new 52 card deck. In order to win, you and your friends know that you need to either score a 21 (blackjack and automatic win) or get a higher total than the dealer. You know that a deck of cards has 13 different cards (2-10, Jack, Queen, King, and Ace), and that there are 4 copies of each in the deck. You know that an ace is equal to either 1 or 11 and that Jacks, Queens, and Kings are worth 10. The dealer deals out the following cards: You: Jack and Ace Friend 1: King and 10 Friend 2: 10 and 10 Dealer: 10 and ? The dealer is about to deal their last card. What are the following probabilities: A) What is the probability that the next card can beat your hand? B) What is the probability that the next card can tie your hand? C) What is the probability that the next card can beat your friends?
- A student planning her curriculum for the upcoming year must select one of three business courses, one of five mathematics courses, two of ten elective courses, and either one of four history courses or one of three social science courses. How many different curricula are available for her consideration? different curriculaSessa, an ancient wise man, visited the king of his nation and showed him a new game. The board was 8 squares by 8 squares. Two players would be given 16 pieces each, lined up on either side of the board. The pieces moved in set ways, and the purpose of the game was to move your pieces to trap the King piece of the other player. As you have probably figured out, Sessa invented chess. His king was utterly delighted at the game - war without bloodshed! - and asked Sessa what he would like in return. In the ancient bombastic style, the King said the request could include up to half of his kingdom. (That was not meant literally.) Sessa asked for the game board to be brought before him. "Highness," he said, "I ask for a grain of rice on the first square. Tomorrow, two grains of rice on the second square. The day after, 4 grains of rice on the third square. On the fourth day, 8 grains of rice. And so on, until the board is full in two months." The king and his ministers laughed…In this game, two chips are placed in a cup. One chip has two red sides and one chip has a red and a blue side. The player shakes the cup and dumps out the chips. The player wins if both chips land red side up and loses if one chip lands red side up and one chip lands blue side up. The cost to play is $4 and the prize is worth $6. Is this a fair game.
- You are a contestant on a game show. There are three closed doors in front of you. The game show host tells you that behind one of these doors is a million dollars in cash, and that behind the other two doors there are trashes. You do not know which doors contain which prizes, but the game show host does. The game you are going to play is very simple: you pick one of the three doors and win the prize behind it. After you have made your selection, the game show host opens one of the two doors that you did not choose and reveals trash. At this point, you are given the option to either stick with your original door or switch your choice to the only remaining closed door. To maximize your chance to win a million dollars in cash, should you switch? Choices: A) Yes B) No C) It doesn't matter because the probability for you to win a million dollars in cash stays the same no matter if you switch or not.If you have 18 dimes and quarters that are worth $2.25, which system would represent this? Ofd+q=18 .10d+.25g 2.25 = Of 18d = q .10d + .25g = 2.25 ofd+q = 2.25 .10d+.25g = 18One hundred extremely intelligent male prisoners are imprisoned in solitary cells and on death row. Each cell is soundproofed and completely windowless. There is a separate room with one hundred small boxes numbered and labeled from 1 to 100. Inside each of these boxes is a slip of paper with one of the prisoners' names on it. Each prisoner's name only appears once and is in only one of the one hundred boxes. The warden decides he is going to play a game with all of the prisoners. If they win, they will all be let free, but if they lose the game, they will all be immediately executed. The hundred prisoners are allowed to enter this separate room with 100 boxes in any predetermined order they wish, but each can only enter the room once and the game ends as soon as the hundredth person enters the room. (At any time, only one prisoner is allowed to enter and remain in this room.) Once a prisoner enters the room, he is allowed to open and look inside as many as Xboxes, where X is a…
