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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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$Many casinos have a game called the Big Six Money Wheel, which has 54 slots featuring a Joker, the casino logo, and various dollar amounts, as shown in the table below. 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. ### Table: Wheel Slot Distribution | Denomination | Number of slots | |-----------------|-----------------| | $40 (Joker) | 1 | | $40 (Casino logo) | 1 | | $20 | 2 | | $10 | 4 | | $5 | 7 | | $2 | 15 | | $1 | 24 | ### Step-by-Step Example **Step 1** Suppose a player bets $18 on the Casino logo denomination. What is the probability of winning this bet? (Write your answer as a fraction.) - Probability of winning: $ \frac{1}{54} $ **Step 2** The (simplified) probability of winning this bet is $ \frac{1}{54} $. What is the probability of losing this bet? (Write your answer as a fraction.) - Probability of losing: $ \frac{53}{54} $ **Step 3** The (simplified) probability of losing this bet is $ \frac{53}{54} $. If a player bets $18 on the Casino logo denomination, find the player's expectation. (Round your answer to two decimal places.) - Expected Value: \$\[ \] (calculation required)$

Transcribed Image Text:Many casinos have a game called the Big Six Money Wheel, which has 54 slots featuring a Joker, the casino logo, and various dollar amounts, as shown in the table below. 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. ### Table: Wheel Slot Distribution | Denomination | Number of slots | |-----------------|-----------------| | $40 (Joker) | 1 | | $40 (Casino logo) | 1 | | $20 | 2 | | $10 | 4 | | $5 | 7 | | $2 | 15 | | $1 | 24 | ### Step-by-Step Example **Step 1** Suppose a player bets $18 on the Casino logo denomination. What is the probability of winning this bet? (Write your answer as a fraction.) - Probability of winning: $ \frac{1}{54} $ **Step 2** The (simplified) probability of winning this bet is $ \frac{1}{54} $. What is the probability of losing this bet? (Write your answer as a fraction.) - Probability of losing: $ \frac{53}{54} $ **Step 3** The (simplified) probability of losing this bet is $ \frac{53}{54} $. If a player bets $18 on the Casino logo denomination, find the player's expectation. (Round your answer to two decimal places.) - Expected Value: \$\[ \] (calculation required)

$## Expectation: Big Six Money Wheel Many casinos have a game called the Big Six Money Wheel, which has 54 slots displaying a Joker, the casino logo, and various dollar amounts, as shown in the table below. Players may bet on the Joker, the casino logo, or one or more dollar denominations. The wheel is spun and if it stops on the same slot as the player's bet, the player wins that amount for each dollar bet. ### Table of Slots | Denomination | Number of Slots | |------------------|-----------------| | $40 (Joker) | 1 | | $40 (Casino logo)| 1 | | $20 | 2 | | $10 | 4 | | $5 | 7 | | $2 | 15 | | $1 | 24 | --- ### Step 1 Suppose a player bets $17 on the $5 denomination. What is the probability of winning this bet? (Write your answer as a fraction.) \[ \frac{7}{54} \] --- ### Step 2 The (simplified) probability of winning this bet is $ \frac{7}{54} $. What is the probability of losing this bet? (Write your answer as a fraction.) \[ \frac{47}{54} \] --- ### Step 3 The (simplified) probability of losing this bet is $ \frac{47}{54} $. If a player bets $17 on the $5 denomination, find the player's expectation. (Round your answer to two decimal places.) \[ \$ \text{[Answer not provided]} \]$

Transcribed Image Text:## Expectation: Big Six Money Wheel Many casinos have a game called the Big Six Money Wheel, which has 54 slots displaying a Joker, the casino logo, and various dollar amounts, as shown in the table below. Players may bet on the Joker, the casino logo, or one or more dollar denominations. The wheel is spun and if it stops on the same slot as the player's bet, the player wins that amount for each dollar bet. ### Table of Slots | Denomination | Number of Slots | |------------------|-----------------| | $40 (Joker) | 1 | | $40 (Casino logo)| 1 | | $20 | 2 | | $10 | 4 | | $5 | 7 | | $2 | 15 | | $1 | 24 | --- ### Step 1 Suppose a player bets $17 on the $5 denomination. What is the probability of winning this bet? (Write your answer as a fraction.) \[ \frac{7}{54} \] --- ### Step 2 The (simplified) probability of winning this bet is $ \frac{7}{54} $. What is the probability of losing this bet? (Write your answer as a fraction.) \[ \frac{47}{54} \] --- ### Step 3 The (simplified) probability of losing this bet is $ \frac{47}{54} $. If a player bets $17 on the $5 denomination, find the player's expectation. (Round your answer to two decimal places.) \[ \$ \text{[Answer not provided]} \]

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Denomination Number of slots $40 (Joker) 1 $40 (Casino logo) 1 $20 2 $10 4 $5 7 $2 15 $1 24 %24