Question
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. Assume a single spin of the roulette wheel is made. Find the probability of winning with the given bet. An example of a line bet is betting that the marble will land in a slot numbered \( 8,9,10,11 \), 12, or 13 . The probability of winning with the given line bet is (Type an integer or a simplified fraction.)
Ask by Chadwick Gardner. in the United States
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The probability of winning with the given line bet is \( \frac{3}{19} \).
Solution
1. There are 38 slots in an American roulette wheel.
2. The line bet covers 6 slots: \(8\), \(9\), \(10\), \(11\), \(12\), and \(13\).
3. The probability of winning is the ratio of the favorable outcomes to the total outcomes:
\[
\text{Probability} = \frac{6}{38}
\]
4. Simplify the fraction by dividing the numerator and denominator by 2:
\[
\frac{6 \div 2}{38 \div 2} = \frac{3}{19}
\]
The probability of winning with the given line bet is \( \frac{3}{19} \).
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Simplify this solution Beyond the Answer
To find the probability of winning with a line bet that includes the numbers 8, 9, 10, 11, 12, and 13, we first note that there are a total of 38 slots on the American roulette wheel. Our line bet covers 6 specific numbers (8, 9, 10, 11, 12, and 13). The probability of winning with this line bet can be calculated using the formula: \[ \text{Probability of Winning} = \frac{\text{Number of Winning Outcomes}}{\text{Total Possible Outcomes}} = \frac{6}{38} \] This fraction simplifies to: \[ \frac{3}{19} \] So, the probability of winning with the given line bet is \( \frac{3}{19} \).
