A roulette wheel has 40 slots around the rim; 38 slots are numbered from 1 to 38 . Half of these 38 slots are red, and the other half are black. T
emaining 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 0.25 of 1
ppposite direction. The ball has an equality likely chance of falling into any one of the 40 slots. Find the probabilities of the events listed in parti
hrough (d) below.
The probability of the event that the ball does not land on a number from 25 through 29 is .
Type an integer or a simplified fraction.)
Ball lands on an even number or on a green slot
The probability of the event that the ball lands on an even number or on a green slot is .
Type an integer or a simplified fraction.)

Ask by Beck Chadwick. in the United States

Jan 22,2025

Question

A roulette wheel has 40 slots around the rim; 38 slots are numbered from 1 to 38 . Half of these 38 slots are red, and the other half are black. T
emaining 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 0.25 of 1
ppposite direction. The ball has an equality likely chance of falling into any one of the 40 slots. Find the probabilities of the events listed in parti
hrough (d) below.
The probability of the event that the ball does not land on a number from 25 through 29 is .
Type an integer or a simplified fraction.)
Ball lands on an even number or on a green slot
The probability of the event that the ball lands on an even number or on a green slot is .
Type an integer or a simplified fraction.)

Ask by Beck Chadwick. in the United States

Jan 22,2025

UpStudy AI · Accepted Answer

To solve the problem, we need to analyze the roulette wheel and the events described.

### Known Conditions:
1. The roulette wheel has 40 slots.
2. Slots numbered from 1 to 38 are divided into:
   - 19 red slots (odd and even numbers)
   - 19 black slots (odd and even numbers)
3. There are 2 green slots: 0 and 00.
4. The ball has an equal chance of landing in any of the 40 slots.

### Part (a): Probability of the ball not landing on a number from 25 through 29
The numbers from 25 to 29 are: 25, 26, 27, 28, 29. This gives us 5 slots.

The total number of slots is 40. Therefore, the number of slots that are not from 25 to 29 is:
$$
40 - 5 = 35
$$

The probability of the ball not landing on a number from 25 to 29 is:
$$
P(\text{not 25 to 29}) = \frac{35}{40} = \frac{7}{8}
$$

### Part (b): Probability of the ball landing on an even number or on a green slot
First, we need to identify the even numbers and the green slots.

**Even Numbers:**
The even numbers from 1 to 38 are: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38. This gives us a total of 19 even numbers.

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

Now, we need to find the total number of favorable outcomes for the event "landing on an even number or on a green slot."

The total number of favorable outcomes is:
$$
\text{Even numbers} + \text{Green slots} = 19 + 2 = 21
$$

Now, we can calculate the probability:
$$
P(\text{even or green}) = \frac{21}{40}
$$

### Summary of Probabilities:
- The probability of the event that the ball does not land on a number from 25 through 29 is $$ \frac{7}{8} $$.
- The probability of the event that the ball lands on an even number or on a green slot is $$ \frac{21}{40} $$.
The probability of the ball not landing on a number from 25 through 29 is $$ \frac{7}{8} $$. The probability of the ball landing on an even number or on a green slot is $$ \frac{21}{40} $$.

Solución de inteligencia artificial de Upstudy

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Solución

Known Conditions:

Part (a): Probability of the ball not landing on a number from 25 through 29

Part (b): Probability of the ball landing on an even number or on a green slot

Summary of Probabilities:

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