The casino game, roulette, allows the gambler to bet on the probability of a ball, which spins in the roulette wheel, landing on a particular color, number, or range of numbers. The table used to place bets contains 38 numbers, and each number is assigned to a color and a range. (Enter your answ fractions.) 3699 E N NNMM 3 00 2. 4 7 Ist Dozen 2nd Dozen 3rd Dozen 1 to 18 EVEN ODD 19 to 36 Part (a) O Part (b) Compute the probability of winning if you bet on one of the dozen groups. a Part (c) Compute the probability of winning if you bet on the range of numbers from 1 to 18. 0.47 O Part (d) Compute the probability of winning if you bet on the range of numbers 19-36. 0.47 Part (e)

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## Understanding Roulette Probability

The casino game Roulette involves betting on the probability of a ball, spun on a roulette wheel, landing on a specific color, number, or range of numbers. The table used for placing bets consists of 38 numbers, each assigned a color and range. Here we will explore different probability scenarios related to a standard Roulette game.

### Roulette Table Layout
A visual representation of a Roulette table shows numbers 1-36, including two additional numbers 0 and 00. The numbers are colored either red or black, except for 0 and 00, which are typically green. The numbers are divided into groups:

1. **1st Dozen (1-12)**
2. **2nd Dozen (13-24)**
3. **3rd Dozen (25-36)**
4. **Columns:** Three separate columns of numbers such as 1-4-7-10-13-16-19-22-25-28-31-34.

### Probability Questions

#### Part (a)
*Compute the probability of winning if you bet on one of the dozen groups.*

- **Answer:** 0.32

#### Part (b)
*Compute the probability of winning if you bet on the range of numbers from 1 to 18.*

- **Answer:** 0.47

#### Part (c)
*Compute the probability of winning if you bet on the range of numbers 19–36.*

- **Answer:** 0.47

#### Part (d)
*Compute the probability of winning if you bet on one of the columns, such as 1-4-7-10-13-16-19-22-25-28-31-34.*

- **Answer:** 0.32

#### Part (e)
*Compute the probability of winning if you bet on the even numbers (excluding zero).*

- **Answer:** 0.47

These calculations are foundational in understanding betting strategies and outcomes in Roulette, providing insights into how probability influences game strategies.
Transcribed Image Text:## Understanding Roulette Probability The casino game Roulette involves betting on the probability of a ball, spun on a roulette wheel, landing on a specific color, number, or range of numbers. The table used for placing bets consists of 38 numbers, each assigned a color and range. Here we will explore different probability scenarios related to a standard Roulette game. ### Roulette Table Layout A visual representation of a Roulette table shows numbers 1-36, including two additional numbers 0 and 00. The numbers are colored either red or black, except for 0 and 00, which are typically green. The numbers are divided into groups: 1. **1st Dozen (1-12)** 2. **2nd Dozen (13-24)** 3. **3rd Dozen (25-36)** 4. **Columns:** Three separate columns of numbers such as 1-4-7-10-13-16-19-22-25-28-31-34. ### Probability Questions #### Part (a) *Compute the probability of winning if you bet on one of the dozen groups.* - **Answer:** 0.32 #### Part (b) *Compute the probability of winning if you bet on the range of numbers from 1 to 18.* - **Answer:** 0.47 #### Part (c) *Compute the probability of winning if you bet on the range of numbers 19–36.* - **Answer:** 0.47 #### Part (d) *Compute the probability of winning if you bet on one of the columns, such as 1-4-7-10-13-16-19-22-25-28-31-34.* - **Answer:** 0.32 #### Part (e) *Compute the probability of winning if you bet on the even numbers (excluding zero).* - **Answer:** 0.47 These calculations are foundational in understanding betting strategies and outcomes in Roulette, providing insights into how probability influences game strategies.
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