5 Unfair gameYou and your five-year-old sister play a game. A fair six-sided die is rolled to determine how manypoints both of you get. (Important: only one die is rolled, not two.)Your score A is the value of the die roll, capped from above at 3: if the die roll is anything 3 orhigher, you get 3 points.Your sister's score B is the value of the same die roll, capped from below at 4: if the die roll isanything 4 or lower, she gets 4 points.Fill in the table of the joint PMF of A and B.A = 1A = 2A = 3|B = 4 B = 5 B = 6Find the range and the probability mass function of B - A, the number of points bywhich your five-year-old sister wins.Find Pr[B = 5| A = 3].

To fill in the joint probability mass function (PMF) of A and B, we need to consider all possible…

Answered: 5 Unfair game ( You and your…

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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Hello, can you please help me solve this problem? Write clearly and neatly on a paper. Upload it here. Thank you. We play a game: You roll a fair die. If it comes up a 4, 5, or 6 on the first roll, you win $80. If not, then you get to roll again. If you get a 4, 5, or 6 on the 2nd roll, you win $40. If not, you get $0. What is the expected amount you will win?
A student receives a test scores of 62, 83 and 91. The students final exam scores is 88 and homework 76 . Each test is worth 20% off the final grade, the final exam is 25 % of the final grade and homework 15% of the final grade. What is the students final grade? A. 90.6 B. 80.6 C. 76.6 D. 85.6
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
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.)
An artist is selling children's crafts. Necklaces cost $2.25 each, and bracelets cost $1.50 per each.Select ALL the combinations of necklaces and bracelets that the artist could sell for exactly $12.00. * 5 necklaces and 1 bracelet 2 necklaces and 5 bracelets 3 necklaces and 3 bracelet 4 necklaces and 2 bracelets 3 necklaces and 5 bracelets 6 necklaces and no bracelets No necklaces and 8 bracelets This is a required question
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 are playing a card game. If you pull an Ace you win $71, if you pull the King of hearts you win $101, if you pull a jack or a queen you win $37, all other pulls you lose. What price should you be charged to make this a fair game? Round your answer to the nearest hundredth.
A game involves drawing a single card from a standard deck. The player receives $10 for an ace, $5 for a king, and $1 for a red card that is neither an ace nor a king. Otherwise, the player receives nothing. If the cost of each draw is $2, should you play? Explain your answer mathematically.
You need to borrow money for gas, so you ask your mother and your sister. You can only borrow money from one of them. Before giving you money, they each say they will make you play a game. Your sister says she wants you to roll a six-sided die. She will give you $⁢4 times the number that appears on the die. Your mother says she wants you to spin a spinner with two outcomes, blue and red, on it. She will give you $⁢5 if the spinner lands on blue and $⁢15 if the spinner lands on red. Determine the expected value of each game and decide which offer you should take. The expected value for your sister's game: $$ The expected value for your mother's game: $$ Which offer should you take?
Dp4
Cycling Race Three friends, Xavier, Yolanda, and Zeke, want to have a race on their stationary bikes. Aware that he is the fastest rider, Xavier claims he can ride n3 miles faster than Yolanda can ride n miles and Zeke can ride log3 n miles, for any value of n. Suppose Xavier's speed is 60 miles per hour, Yolanda's speed is 20 miles per hour, and Zeke's speed is 3 miles per hour. We will show that Xavier is incorrect (he has never taken a Discrete Structures course, evi- dently!). (a) How large must n be to ensure that Yolanda finishes before Xavier? Justify the answer. (b)How large must n be to ensure that Zeke finishes before Xavier? Justify the answer. (c) As n gets increasingly large, who completes their ride first, Zeke or Yolanda? Justify The answer. Answer:
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?

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