You
(A) If you select a row by drawing a single card and your friend selects a column by drawing a single card (after replacement), what is your expected value of the game?
(B) If your opponent chooses an optimal strategy (ignoring the cards) and you make your row choice by drawing a card, what is your expected value?
(C) If you both disregard the cards and make your own choices, what is your expected value, assuming that you both choose optimal strategies?
Want to see the full answer?
Check out a sample textbook solutionChapter 11 Solutions
Finite Mathematics for Business, Economics, Life Sciences and Social Sciences
Additional Math Textbook Solutions
Excursions in Modern Mathematics (9th Edition)
A Survey of Mathematics with Applications (10th Edition) - Standalone book
Mathematics with Applications In the Management, Natural and Social Sciences (11th Edition)
Using & Understanding Mathematics: A Quantitative Reasoning Approach (7th Edition)
Fundamentals of Differential Equations and Boundary Value Problems
Calculus for Business, Economics, Life Sciences, and Social Sciences (13th Edition)
- This game is called “Get Negative”. Roll two dice (record these in the order you roll them), and then do then do the following: take the first number rolled and subtract 2 times the second number rolled. Regardless of who rolls, Player A gets 3 points if the product is greater than or equal to 0 (i.e. it is zero or positive); Otherwise Player B gets 1 points. The players may or may not take turns rolling the dice as it does not matter who is rolling. Any player may score on any roll, and every roll will result in a score. Play the game by rolling the dice 25 times. For each turn, keep a record of both dice and the resulting answer and the points scored, according to the rules above. Tally the points and calculate the final score for each player. Remember, someone gets a point for each turn, depending on the numbers rolled. (One does not have to be rolling to receive the points.) (Note: you may test the game by yourself by doing all of the 25 rolls yourself and just giving the…arrow_forwardMakalya is playing a game using a wheel divided into eight equal sections, as shown in the diagram below. Each time the spinner lands on brown or orange, she will win a prize. Simplify your answer. Brown White Green Orange Yellow Brown Brown White P (brown or orange) = [Select ] %3D P (brown first then orange) = [ Select ] %3D DELLarrow_forwardIf A and B are nxn matrices .Find the cost of calculating A? + BAB.arrow_forward
- 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.arrow_forwardZara 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.arrow_forwardOrange M&M's: The M&M's web site says that 20% of milk chocolate M&M's are orange. Let's assume this is true and set up a simulation to mimic buying 200 small bags of milk chocolate M&M's. Each bag contains 55 candies. We made this dotplot of the results. The number of orange M&M's was counted and here is a dotplot of the results: $800 0.0 0.1 0.2 0.3 Proportion_Orange An error in the simulation 0.4 Which of the following reasons best explains the variability we see in the proportion of orange M&M's in the bags? The random selection of samples Human error in calculating the proportion of orange M&M's in a bag Poor quality control in the production process 0.5arrow_forward
- Blackjack: In single-deck casino blackjack, the dealer is dealt two cards from a standard deck of 52. The first card is dealt face down and the second card is dealt face up. QUESTION: Of the 52 cards in the deck, four are aces and 16 others (kings, queens, jacks, and tens) are worth 10 points each. The dealer has a blackjack if one card is an ace and the other is worth 10 points; it doesn't matter which card is face up and which card is face down. How many different blackjack hands are there? There are _____ blackjack hands possible.arrow_forwardThe game of craps is played with two dice. The player rolls both dice and wins immediately if the outcome (the sum of the faces) is 7 or 11. If the outcome is 2, 3, or 12, the player loses immediately. If he rolls any other outcome, he continues to throw the dice until he either wins by repeating the first outcome or loses by rolling a 7.arrow_forwardKiara and her friends are playing The Duck Game at a local fair. In this game, the player selects one of 50 identical plastic ducks from a pool. The bottom of each duck is numbered 1, 2, or 3. If you draw a duck with a 1, you win a small prize, a duck with a 2 will win you a medium prize, and a duck with a 3 will win a large prize. According to the game operator, there are 25 ducks with the number 1 on the bottom, 20 ducks with the number 2, and 5 ducks with the number 3. Use the information given to explore some of the mathematical concepts you have practiced so far by answering the questions below. Suppose that Kiara plays The Duck Game once. What is the probability that she draws a duck with the number 3 on the bottom? Explain the process you used to solve this question. Kiara draws a duck with a 1 on her first try and decides to play the game again. This time her friends Denny and Rayanna play the game with her. Each friend takes a turn drawing a duck from the pond. Once all…arrow_forward
- A particular two-player game starts with a pile of diamonds and a pile of rubies. Onyour turn, you can take any number of diamonds, or any number of rubies, or an equalnumber of each. You must take at least one gem on each of your turns. Whoever takesthe last gem wins the game. For example, in a game that starts with 5 diamonds and10 rubies, a game could look like: you take 2 diamonds, then your opponent takes 7rubies, then you take 3 diamonds and 3 rubies to win the game.You get to choose the starting number of diamonds and rubies, and whether you gofirst or second. Find all starting configurations (including who goes first) with 8 gemswhere you are guaranteed to win. If you have to let your opponent go first, what arethe starting configurations of gems where you are guaranteed to win? If you can’t findall such configurations, describe the ones you do find and any patterns you see.arrow_forwardINSTRUCTIONS: Solve the following puzzles by filling in the matrix as discussed. At a recent birthday party there were four mothers and their children aged 1, 2, 3 and 4. It was Julia's child's birthday party. Brent is not the oldest child. Samantha had Arthur just over a year ago. Linda's child will be 3 next birthday. Dennis is older than Chris. Tessa's child is the oldest. Chris is older than Linda's child. Can you work out whose child is whose and their relevant ages?arrow_forwardRock smashes scissors Almost everyone has played the rock-paper- scissors game at some point. Two players face each other and, at the count of 3, make a fist (rock), an extended hand, palm side down (paper), or a "V" with the index and middle fingers (scissors). The winner is determined by these rules: rock smashes scissors; paper covers rock; and scissors cut paper. If both players choose the same object, then the game is a tie. Suppose that Player 1 and Player 2 are both equally likely to choose rock, paper, or scissors. (a) Give a probability model for this chance process. (b) Find the probability that Player 1 wins the game on the first throw. 3.arrow_forward
- College AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning