Step 1 :The total number of slots in American roulette is 38. These slots are numbered 1 to 36, with two additional slots labeled 0 and 00 that are painted green. The numbers 0 and 00 are considered neither even nor odd. Half of the remaining slots are colored red and half are black.
Step 2 :We are asked to find the probability of the marble landing on a green or odd slot in a single spin of the roulette wheel.
Step 3 :The total number of green slots is 2 (0 and 00).
Step 4 :The total number of odd slots is half of the remaining 36 slots, which is 18.
Step 5 :We need to find the probability of the marble landing on a green or odd slot. This means we need to add the number of green slots and odd slots together. Since 0 and 00 are considered neither even nor odd, we don't have to worry about double counting. So, the total number of favorable outcomes is \(2 + 18 = 20\).
Step 6 :The probability of an event is the number of favorable outcomes divided by the total number of outcomes. So, we need to divide 20 by 38 to find the probability.
Step 7 :Using the formula for probability, we get \(\frac{20}{38} = 0.5263157894736842\).
Step 8 :Final Answer: The probability of the marble landing on a green or odd slot is approximately \(\boxed{0.526}\).