day, Fred and his N friends were playing a card game in which each player throws a card with a number written on it. The cards are such that a number X is written on front of the card, and the negative of that number is written on the back side of the card. This game has the following rules: - Each of the N players is asked to throw a card. After all the N cards are thrown, Fred has to flip one or more cards in consecutive order, only orice. Your task is to help Fred flip the cards in such a way that the sum of the numbers, on front face of the cards, is the maximum

day, Fred and his N friends were playing a card game in which each player throws a card with a number written on it. The cards are such that a number X is written on front of the card, and the negative of that number is written on the back side of the card. This game has the following rules: - Each of the N players is asked to throw a card. After all the N cards are thrown, Fred has to flip one or more cards in consecutive order, only orice. Your task is to help Fred flip the cards in such a way that the sum of the numbers, on front face of the cards, is the maximum

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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Maria plays the following game: There is a jar containing 2 gold coins, 2 silver coins, and 6 bronze coins. She must select two coins. She gets $2 for each gold coin she selects. She gets $1 for each silver coin she selects. She gets nothing for selecting bronze coins. For example, if she picks one gold and one silver coin, she will get $3 total. If she picks one silver and one bronze coin, she gets $1 total. Let X be her winnings for this game. Fill in the pmf table (leave your answers here as fractions). x 0 1 2 3 4 p(x) Compute the expected value. Write your answer as a decimal (as you would a dollar amount): $ .
Suppose there is a game in which you throw a die first and then you toss a coin. However, you will toss a coin once if the die shows an even number. Conversely, you will toss a coin thrice if the die shows an odd number. Use the notation 4H, for example, to denote the outcome that the die comes up 4 and then the coin comes up heads, and 3HHH to denote the outcome that the die comes up 3 followed by 3 heads in succession, construct a tree diagram of the sample space.
You are playing the new Lemon Game at Vegas. There are 3 windows in the slot machine. Window 1 displays only one of two choices: lemon or strawberry. Window 2 can display three choices: lemon, strawberry, or blueberry. Window 3 can display three choices: lemon, papaya, or cherry. Windows spin randomly and independent from each other. To win $1 you must have one lemon showing. To win $2, you must have two lemons, and to win the $5 jackpot, you must have all windows showing lemons. Using a tree diagram, determine the sample space. Determine the probability distribution. Let the random variable X represent the number of lemons displayed during one spin. Calculate the mean and standard deviation of the distribution. In four sentences or less, would you want to play this game if it cost $.50 per spin? Justify your answer using the expected value approach.
The game Capture is played by two players, First and Second, who take turns to move towards one another on a narrow bridge. Initially, the two players are at opposite ends of the bridge, at a distance of n feet from each other. (Here n is an arbitrary positive integer.) When it is their turn, they are allowed to jump 1, 2, or 3 feet toward each other. The game starts by First making a move first; the game is over when one player is able to capture (jump on top of) the other player. Generalize the problem further to the case when the initial distance is n feetand the players are allowed to jump any (positive) integer number of feet up to k feet. (Here n and k are arbitrary natural numbers.)
Makalya 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 DELL
For his Carnival project, Chester designed a game where players pick a random marble from a bag. In the bag there are 2 pink marbles, 10 green marbles, and 8 white marbles. If players draw a pink marble they get a large candy bar prize, if they draw a green marble they get a small lollipop prize, and if they draw a white marble they get a fist bump. Chester purchased a set of 16 candy bars for $12 and a bag of 200 lollipops for $20. Answer the following questions: What is Chester's expected cost per game? $ If Chester plans for 40 people to play his game, How many candy bars should he expect to give out? How many lollipops should he expect to give out?
: The first week of chess club had 3 students. The second week had five students. The third week had eight students and the fourth had twelve. If this pattern continues, how many students will show up for the eight weeks?
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?
Jennifer has 25 books on her bookshelf. She has 10 fiction books, and the rest are non-fiction books. If Jennifer selects a book at random, which expression represents the probability that the book she selects will be a non-fiction book? ASAP PLS.
In a certain card game, for every 4 blue cards, there are 3 yellow cards. There are a total of 84 blue and yellow cards in the game.
To raise money for the local Veterans Affairs hospital, your friend organizes a fundraiser, inviting you to play a two-stage game where you pay $8 to play. The game works as follows: a fair 8-sided die is rolled, noting the number shown, and a spinner divided into 4 equal regions of different colors (blue, red, green, orange) is spun, noting the color. If the die shows 3 or the spinner shows orange, then you win $21. If the die shows an even number and the spinner does not show orange, then you win $9. Otherwise, you do not win anything. Let X be your net winnings. (a) Create a probability distribution for X. Enter the possible values of X in ascending order from left to right. All probabilities should be exact. X P(X) (b) Compute your expected net winnings for the game. Round your answer to the nearest cent. $ (c) Is this game fair? Yes No
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?