A roulette wheel has 40 slots around the rim, 38 slots are numbered from 11 to 38 . Half of these 38 slots are red, and the other half are black. The
remaining 2 slots are numbered 0 and 00 and are green. As the rouleme wheel is spun in one direction, a small ivory ball is rolled along the rim in
opposite 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 parts (
through (d) below.
c. Ball does not land on a number from 25 through 29
The probability of the event that the ball does not land of a number from 25 through 29 is
(Type an integer or a simplified fraction.)
d. 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 Henry Colon. in the United States

Jan 22,2025

Question

A roulette wheel has 40 slots around the rim, 38 slots are numbered from 11 to 38 . Half of these 38 slots are red, and the other half are black. The
remaining 2 slots are numbered 0 and 00 and are green. As the rouleme wheel is spun in one direction, a small ivory ball is rolled along the rim in
opposite 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 parts (
through (d) below.
c. Ball does not land on a number from 25 through 29
The probability of the event that the ball does not land of a number from 25 through 29 is
(Type an integer or a simplified fraction.)
d. 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 Henry Colon. in the United States

Jan 22,2025

UpStudy AI · Accepted Answer

To determine the probability that the ball lands on an even number or on a green slot, let's break down the components:

1. **Total Slots:** There are 40 slots in total.
   - **Numbered Slots:** 38 slots are numbered from 11 to 38.
     - **Even Numbers:** The even numbers between 11 and 38 are 12, 14, 16, ..., 38. 
       - The number of even numbers can be calculated as:
         $$
         \text{Number of even numbers} = \frac{38 - 12}{2} + 1 = 14
         $$
       - **Probability of landing on an even number:**
         $$
         P(\text{Even Number}) = \frac{14}{40} = \frac{7}{20}
         $$
   - **Green Slots:** There are 2 green slots (0 and 00).
     - **Probability of landing on a green slot:**
       $$
       P(\text{Green Slot}) = \frac{2}{40} = \frac{1}{20}
       $$

2. **Combined Probability:** Since landing on an even number and landing on a green slot are mutually exclusive events (they cannot happen simultaneously), the combined probability is the sum of the individual probabilities.
   $$
   P(\text{Even Number or Green Slot}) = P(\text{Even Number}) + P(\text{Green Slot}) = \frac{7}{20} + \frac{1}{20} = \frac{8}{20} = \frac{2}{5}
   $$

**Final Answer:**
$$
\frac{2}{5}
$$
The probability of the ball landing on an even number or on a green slot is $$ \frac{2}{5} $$.

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