When playing American roulette, the croupier (attendant) spins a marble that lands in one of the 38 slots in a revolving turntable. The slots are numbered 1 to 36, with two additional slots labeled 0 and 00 that are painted green. Consider the numbers 0 and 00 as neither even nor odd. Half the remaining slots are colored red and half are black. Assume a single spin of the roulette wheel is made. Find the probability of the marble landing on a green or odd slot. The probability of the marble landing on a green or odd slot is (Type an integer or a simplified fraction.)
When playing American roulette, the croupier (attendant) spins a marble that lands in one of the 38 slots in a revolving turntable. The slots are numbered 1 to 36, with two additional slots labeled 0 and 00 that are painted green. Consider the numbers 0 and 00 as neither even nor odd. Half the remaining slots are colored red and half are black. Assume a single spin of the roulette wheel is made. Find the probability of the marble landing on a green or odd slot. The probability of the marble landing on a green or odd slot is (Type an integer or a simplified fraction.)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:**Understanding Probability in American Roulette**
When playing American roulette, the croupier (attendant) spins a marble that lands in one of the 38 slots on a revolving turntable. The slots are numbered 1 to 36, with two additional slots labeled 0 and 00 that are painted green. Consider the numbers 0 and 00 as neither even nor odd. Half the remaining slots are colored red and half are black.
**Objective:**
Assume a single spin of the roulette wheel is made. Find the probability of the marble landing on a green or odd slot.
**Solution Guide:**
- **Total Slots:** 38 (Numbers 1 to 36, plus 0 and 00)
- **Green Slots:** 2 slots (0 and 00)
- **Odd Slots:** Any odd number between 1 and 36. There are 18 odd numbers (1, 3, 5, ..., 35).
Calculating probability involves finding the successful outcomes over the total possible outcomes.
- **Successful Outcomes (Green or Odd):**
- Green: 2
- Odd: 18
- Total (Green or Odd): 2 (green) + 18 (odd) = 20
- **Probability:**
- The probability of landing on a green or odd slot = Total successful outcomes / Total possible outcomes
- Probability = 20 / 38
- Simplify the fraction: 10 / 19
Therefore, the probability of the marble landing on a green or odd slot is \( \frac{10}{19} \). This fraction represents the possible outcomes that are favorable for landing on either a green or odd-numbered slot.
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