A roulette wheel has 34 slots around the rim; 32 slots are numbered from 1 to 32 . Half of these 32 slots are red, and the
other half are black. The remaining 2 slots are numbered 0 and 00 and are green. As the roulette wheel is spun in
one direction, a small ivory ball is rolled along the rim in the opposite direction. The ball has an equality likely chance of
falling into any one of the 34 slots. Find the probabilities of the events listed in parts (a) through (d) below.
a. Ball lands in a red slot
The probability of the event that the ball lands in a red slot is .
(Type an integer or a simplified fraction.)
b. Ball lands on 0 or 32
The probability of the event that the ball lands on 0 or 32 is .
(Type an integer or a simplified fraction.)
c. Ball does not land on a number from 6 through 28
The probability of the event that the ball does not land on a number from 6 through 28 is .
(Type an integer or a simplified fraction.)
d. Ball lands on an odd number or on a green slot
The probability of the event that the ball lands on an odd number or on a green slot is
(Type an integer or a simplified fraction.)

Ask by Page Johnston. in the United States

Jan 23,2025

Question

A roulette wheel has 34 slots around the rim; 32 slots are numbered from 1 to 32 . Half of these 32 slots are red, and the
other half are black. The remaining 2 slots are numbered 0 and 00 and are green. As the roulette wheel is spun in
one direction, a small ivory ball is rolled along the rim in the opposite direction. The ball has an equality likely chance of
falling into any one of the 34 slots. Find the probabilities of the events listed in parts (a) through (d) below.
a. Ball lands in a red slot
The probability of the event that the ball lands in a red slot is .
(Type an integer or a simplified fraction.)
b. Ball lands on 0 or 32
The probability of the event that the ball lands on 0 or 32 is .
(Type an integer or a simplified fraction.)
c. Ball does not land on a number from 6 through 28
The probability of the event that the ball does not land on a number from 6 through 28 is .
(Type an integer or a simplified fraction.)
d. Ball lands on an odd number or on a green slot
The probability of the event that the ball lands on an odd number or on a green slot is
(Type an integer or a simplified fraction.)

Ask by Page Johnston. in the United States

Jan 23,2025

UpStudy AI · Accepted Answer

To solve part (d), we need to determine the probability that the ball lands on an **odd number** or on a **green slot**.

### **Details of the Roulette Wheel:**
- **Total Slots:** 34
  - **Numbered Slots:** 32 (numbered from 1 to 32)
    - **Red Slots:** 16
    - **Black Slots:** 16
  - **Green Slots:** 2 (numbered 0 and 00)

### **Calculating the Probability:**

1. **Odd Numbers:**
   - The numbers range from 1 to 32.
   - **Number of Odd Numbers:** 16 (since half of the numbers from 1 to 32 are odd).

2. **Green Slots:**
   - There are 2 green slots: 0 and 00.

3. **Total Favorable Outcomes:**
   - **Odd Numbers:** 16
   - **Green Slots:** 2
   - **Total:** $$ 16 + 2 = 18 $$

4. **Total Possible Outcomes:**
   - 34 slots in total.

5. **Probability:**
   $$
   \text{Probability} = \frac{\text{Favorable Outcomes}}{\text{Total Possible Outcomes}} = \frac{18}{34}
   $$
   - Simplifying the fraction:
   $$
   \frac{18}{34} = \frac{9}{17}
   $$

### **Final Answer:**
$$
\boxed{\dfrac{9}{17}}
$$
The probability that the ball lands on an odd number or on a green slot is $$ \frac{9}{17} $$.

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