Questions: 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 00 or red slot. The probability of the marble landing on a 00 or red 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 00 or red slot. The probability of the marble landing on a 00 or red slot is (Type an integer or a simplified fraction.)
Transcript text: 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 00 or red slot. The probability of the marble landing on a 00 or red slot is $\square$ (Type an integer or a simplified fraction.)
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Solution

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Solution Steps

Step 1: Determine the Total Number of Slots

In American roulette, there are a total of 38 slots. These include numbers 1 to 36, and two additional slots labeled 0 and 00.

Step 2: Identify the Slots of Interest

We are interested in the probability of the marble landing on a 00 or a red slot. There is 1 slot for 00. Half of the remaining 36 slots (1 to 36) are red, which means there are 18 red slots.

Step 3: Calculate the Probability

The number of favorable outcomes (landing on 00 or a red slot) is the sum of the number of red slots and the 00 slot:

\[ 1 \, (\text{for 00}) + 18 \, (\text{red slots}) = 19 \]

The probability of landing on a 00 or a red slot is the number of favorable outcomes divided by the total number of slots:

\[ \frac{19}{38} \]

Final Answer

The probability of the marble landing on a 00 or red slot is \(\boxed{\frac{19}{38}}\).

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