**An American roulette wheel has 38 slots: two slots are numbered 0 and 00, and the remaining slots are numbered from 1 to 36. What is the probability that the ball lands in an even-numbered slot. In roulette, 0 and 00 are considered neither even nor odd.**

To find the probability that the ball lands in an even-numbered slot on an American roulette wheel, let's break it down step by step.

### Total slots:
- The American roulette wheel has **38 slots** in total, including the numbers 0 and 00.

### Even-numbered slots:
- The numbers from 1 to 36 alternate between odd and even.
- The even numbers in this range are:  
  2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, and 36.  
  This gives us **18 even-numbered slots**.

### Favorable outcomes:
- The number of even-numbered slots is **18**.
- The slots 0 and 00 are neither even nor odd, so they are excluded from this count.

### Probability calculation:
The probability \( P \) that the ball lands on an even-numbered slot is given by the ratio of favorable outcomes (even-numbered slots) to the total number of slots:
\[
P = \frac{\text{Number of even-numbered slots}}{\text{Total number of slots}} = \frac{18}{38}
\]

Simplifying this fraction:
\[
P = \frac{9}{19}
\]

Thus, the probability that the ball lands in an even-numbered slot is \( \frac{9}{19} \), or approximately **0.4737** (or **47.37%**).

---

Would you like more details on any part of this explanation? Here are some related questions for further understanding:

1. What is the probability that the ball lands in an odd-numbered slot?
2. How does the presence of 0 and 00 affect the overall odds in roulette?
3. What is the probability of landing on a red or black slot in American roulette?
4. How does European roulette differ in terms of probabilities?
5. What is the house edge in American roulette, and how is it calculated?

**Tip:** In roulette, the presence of 0 and 00 slots increases the house's advantage, since these slots are excluded from simple even-odd or red-black bets.

An American roulette wheel has 38 slots: two slots are numbered 0 and 00, and the remaining slots are numbered from 1 to 36. What is the probability that the ball lands in an even-numbered slot? In roulette, 0 and 00 are considered neither even nor odd.

Discover how to calculate the probability of landing on an even-numbered slot in American roulette. This problem uses fundamental probability concepts and involves a detailed breakdown of favorable outcomes versus total outcomes. Suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation