A roulette wheel has 40 slots around the rim; 38 slots are numbered from 1 to 38. Half of these 38 slots are red, and the other half are black. The remaining 2 slots are numbered 0 and 00 and are green. As the roulette wheel is spun in one direction, a small ivory ball is rolled along the rim in the opposite direction. The ball has an equality likely chance of falling into any one of the 40 slots. Find the probabilities of the events listed in parts (a) through (d) below.

To calculate the probabilities for the events related to a roulette wheel, we start by noting that there are 40 slots in total: 18 red, 18 black, and 2 green (0 and 00). (a) **Probability of landing on red:** The probability \( P(\text{red}) \) is calculated by dividing the number of favorable outcomes (red slots) by the total number of slots: \[ P(\text{red}) = \frac{18}{40} = \frac{9}{20} \approx 0.45 \text{ or } 45\% \] (b) **Probability of landing on black:** Similarly, the probability \( P(\text{black}) \) is: \[ P(\text{black}) = \frac{18}{40} = \frac{9}{20} \approx 0.45 \text{ or } 45\% \] (c) **Probability of landing on green:** For landing on green, which includes both 0 and 00: \[ P(\text{green}) = \frac{2}{40} = \frac{1}{20} = 0.05 \text{ or } 5\% \] (d) **Probability of landing on a number greater than 18:** The numbers greater than 18 on the wheel are 19 to 38, which gives us 20 favorable outcomes: \[ P(\text{greater than 18}) = \frac{20}{40} = \frac{1}{2} = 0.5 \text{ or } 50\% \] In summary, the probabilities are: - Red: 45% - Black: 45% - Green: 5% - Greater than 18: 50%