14In a competition between players A and B, the first player to win two games in a row or a totalof three games wins. How many ways can the competition be played if A wins the first gameand B wins the second game? O463.

Let us assume there are three students A, B and C sitting beside each other. The different ways in…

Answered: In a competition between players A and…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Dodgeball There is a dodgeball tournament with 8 teams. The committee has decided the best way to decide who the best team is to have each team play each other once. 1. How many games will there be? 2. If there were 10 teams, how many might there be? 3. How might you find out if there were 100? Or 222? (You do not have to solve. Just explain or show how you would find it.)
Three players enter a room and are given a red or a blue hat to wear. The color of each hat is determined by a fair coin toss. Players cannot see the color of their own hats, but do see the color of the other two players' hats. The game is won when at least one of the players correctly guesses the color of his own hat and no player gives an incorrect answer. In addition to having the opportunity to guess a color, players may also pass. Communication of any kind between players is not permissible after they have been given hats; however, they may agree on a group strategy beforehand. The players decided upon the following strategy. A player who sees that the other two players wear a hat with the same color guesses the opposite color for his/her own hat; otherwise, the player says nothing. What is the probability of winning the game under this strategy?
At a county fair, you pay $2 to play the following game: You are given a fair coin, and two bags standin front of you, labelled Bag A and Bag B. You flip a coin: If your coin lands Heads, you pick a ballfrom Bag A. If your coin lands tails, you pick a ball from Bag B. Each ball has a dollar value written onit, and you win the number of dollars shown on the ball. • Bag A contains four (4) balls in total: Three (3) balls show $1, and one (1) ball shows $5.• Bag B contains three (3) balls in total: Two (2) balls show $2, and one (1) ball shows $3.You WIN money if you leave with more money than you started with. You LOSE money if you leavewith less money than you started with. You BREAK EVEN if you leave with the same money that youstarted with.Let H denote the event that you flip heads, T denote the event that you flip tails, W the event that youwin, and L the event that you lose.(i) You pay to play exactly one game. What is the probability that you WIN given thatyou flipped a Heads?(ii)…
Zara and Sue play the following game. Each of them roll a fair six-sided die once. If Sue’s number is greater than or equal to Zara’s number, she wins the game. But if Sue rolled a number smaller than Zara’s number, then Zara rolls the die again. If Zara’s second roll gives a number that is less than or equal to Sue’s number, the game ends with a draw. If Zara’s second roll gives a number larger than Sue’s number, Zara wins the game. Find the probability that Zara wins the game and the probability that Sue wins the game. Note: Sue only rolls a die once. The second roll, if the game goes up to that point, is made only by Zara.
You have been asked to play a card game. A card is dealt from a complete deck offifty-two cards (no jokers). A deck has 4 aces, 4 kings, 4 queens, 4 jacks, and 36 other cards.It works like this:• If the card is a ace, you lose $4.• If the card is a king or jack, you lose $10.• If the card is a queen, you win $8.• If the card is anything else, you win $1.Find the expected value of the game. Write the excepted value rounded to the nearest cent
A bag contains 16 red coins, 8 blue coins, and 8 green coins. A player wins by pulling a red coin from the bag. Is this game fair?
Toward the end of a game of Scrabble you hold the letters D,O,G and Q. You can choose three of these four letters and arrange them in order in how many different ways?
Player pays a fee, then reaches into a large jar and picks out a ball. The jar contains one ball for each letter of the alphabet. If the players picks out a ball with a vowel on it, the player wins 500 dollars. If the player picks out a ball with a consonant on it, the player wins nothing. What fee should be charged to play this game in order for it to be considered a fair game?
2. The college's soccer team will play II games next fall. Each game can result in one of three outcomes: a win, a loss, or a tie. Find the total possible number of outcomes for the season record.
Jon flips a coin and writes down H of heads comes up or T if tails comes up. He does this 3 times. If the order of the results matters, how many possible outcomes are there? 8 9 4 6
In the board game Clue, the object of the game is to determine the which character is the murderer, whichweapon was used and in which room the murder took place (e.g., “Colonel Mustard with the Candlestickin the Library”). There are 6 different characters, 6 weapons, and 9 rooms. How many different outcomesare possible?

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In a competition between players A and B, the first player to win two games in a row or a total of three games wins. How many ways can the competition be played if A wins the first game and B wins the second game? O 4 O 5 O 3