The following gambling game, known as the wheel of fortune (or chuck-a-luck), is quite popular at many carnivals and gambling casinos: A player bets on one of the numbers 1 through 6. Three dice are then rolled, and if the number bet by the player appears i times, i = 1, 2, 3, then the player wins i units; if the number bet by the player does not appear on any of the dice, then the player loses 1 unit. Is this game fair to the player? Do all the work with fractions (do not use decimals).

The following gambling game, known as the wheel of fortune (or chuck-a-luck), is quite popular at many carnivals and gambling casinos: A player bets on one of the numbers 1 through 6. Three dice are then rolled, and if the number bet by the player appears i times, i = 1, 2, 3, then the player wins i units; if the number bet by the player does not appear on any of the dice, then the player loses 1 unit. Is this game fair to the player? Do all the work with fractions (do not use decimals).

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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A particular gambling game pays 4 to 1 and has a 20% chance to win. Someone will bet $10, 125 times, and keep track of the total amount won or lost. Which of the following boxes will produce the right answers? Check ALL answers that apply. a. 1 ticket labeled $10 and 4 tickets labeled -$10 b. 20 tickets labeled $10 and 80 tickets labeled -$10 c. 20 tickets labeled 1 and 80 tickets labeled 0 d. 1 ticket labeled $40 and 4 tickets labeled -$10 e. 20 tickets labeled $40 and 80 tickets labeled -$10 f. 1 ticket labeled 1 and 4 tickets labeled 0
Problem 2 A box of bolts contains eight thick bolts, five medium bolts, and three thin bolts. A box of nuts contains six that fit the thick bolts, four that fit the medium bolts, and two that fit the thin bolts. One bolt and one nut are chosen at random. What is the probability that the nut fits the bolt?
QUESTION 10. A casino offers a game that it calls "five in a row". The rules of the game are simple: Pick a color, either red or black. Take a well-shuffled ordinary deck of 52 cards and pick 5 cards anywhere in the deck. If you pick 5 in a row of the color you chose, you win. Otherwise, you lose. You have to pay $10 for the chance to play this game, and you get $360 if you win. A standard deck has 26 red cards and 26 black cards. 60 971 to nois91 123W Calculate the expected value of playing this game in the casino. In other words, for each $10 that you spend in order to play this game, how much money should you expect to win back? noiges
Question 15 Keisha has a bag with 8 balls numbered 1 through 8 . She is playing a game of chance. This game is this: Keisha chooses one ball from the bag at random. She wins $1 if the number 1 is selected, $2 if the number 2 is selected, $5 if the number 3 is selected, $6 if the number 4 is selected, $8 if the number 5 is selected, and $10 if the number 6 is selected. She loses $14 if 7 or 8 is selected. (a) Find the expected value of playing the game. dollars (b) What can Keisha expect in the long run, after playing the game many times?(She replaces the ball in the bag each time.) Keisha can expect to gain money. Shecanexpecttowindollarsperselection. Keisha can expect to lose money. Shecanexpecttolosedollarsperselection. Keisha can expect to break even (neither gain nor lose money).…
Many casinos have a game called the Big Six Money Wheel, which has 54 slots in which are displayed a Joker, the casino logo, and various dollar amounts, as shown in the table at the top of the next column. Players may bet on the Joker, the casino logo, or one or more dollar denominations. The wheel is spun and if the wheel stops on the same place as the player's bet, the player wins that amount for each dollar bet. Denomination Number of slots $40 (Joker) 1 $40 (Casino logo) 1 $20 2 $10 4 $5 7 $2 15 $1 24 If a player bets $4 on the $10 denomination, find the player's expectation. (Round your answer to two decimal places.)
Problem 4. You are to play the following game of cards. Cards are worth their face value, Jacks, Queens and Kings are also worth 10 and Aces are worth 11. You pull precisely two cards from a standard deck and if their sum is at least 20, then you win the game and are given a prize of cash. It costs you $10 to play the game. At least how much should the prize be in order to make your expected winnings positive? Note that if the sum of your cards is less than 20 then you lose your $10.
Solve the following problem, similar to problem 4 from section 2.4 of your text. You select 9 cards randomly from a deck of 52 cards. What is the probability that all of the cards selected are face cards (i.e. jacks, queens, or kings)?
What theorems and principles are employed to solve the following riddle: Ten band members have had their musical instruments placed randomly within boxes. Each band member gets five shots at opening boxes, trying to find their own instrument. (Thus, a 50% chance of each individual finding the desired instrument.) They're not allowed to communicate about what they find. If the entire band fails to find their instruments, they're all fired...and the odds of them all finding their instruments via random guessing is 1 in 1,024. But the drummer has an idea that will radically increase their odds of success. What theorems and principles would you need to employ to solve the riddle. Solving the riddle is not the question. What are the methods (proof by contraposition, would be an example) Rules :• Instruments have been randomly placed in 10 boxes.• The pictures on the boxes don't necessarily correspond to the instruments inside.• Each musician can open up to 5 boxes, and they have to…
QUESTION 10. A casino offers a game that it calls "five in a row". The rules of the game are simple: Pick a color, either red or black. Take a well-shuffled ordinary deck of 52 cards and pick 5 cards anywhere in the deck. If you pick 5 in a row of the color you chose, you win. Otherwise, you lose. You have to pay $10 for the chance to play this game, and you get $360 if you win. A standard deck has 26 red cards and 26 black cards. Calculate the expected value of playing this game in the casino. In other words, for each $10 that you spend in order to play this game, how much money should you expect to win back? Insbuie sdorli yilidad og in Colomal aw drabute sib yillidsdorg sdt belle betov trebutz & Jerit nevid d sicbibnso trons not bistov to sisM zew Insbute 6383 lidsdong and brid bns eloy Jo doig ar zi 15/W b 29110g016 HAS
If someone were to bet $1 on the second dozen numbers (which pays 2 to 1) in the game of roulette 33 seperate times, what is the chance that they would end up losing money?
Problem 1 The University of Oklahoma has a renowned radar research program within the School of Electrical and Computer Engineering. Say that there are two radar prototypes under development, A1 and A2, and the effectiveness of each is determined by their ability to spatially detect a particular object. A1 has a probability of 0.5 of detecting the object, and A2 has probability 0.3 of detecting the object. a. Find the probability that the object is detected. b. Find the probability that the object is detected by exactly one of the radar prototypes. c. Given that the object was detected by exactly one of the prototypes, find the probability that it was A1 that detected it.
A combination lock requires the user to turn four wheels, each with the digits 0 to 9. What are the odds against two locks having the same combination?