A roulette wheel has 34 slots around the rim; 32 slots are numbered from 1 to 32 . Half of these 32 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 34 slots. Find the probabilities of the events listed in parts (a) through (d) below. a. Ball lands in a red slot The probability of the event that the ball lands in a red slot is \( \frac{8}{17} \). (Type an integer or a simplified fraction.) b. Ball lands on 0 or 32 The probability of the event that the ball lands on 0 or 32 is \( \frac{1}{17} \). (Type an integer or a simplified fraction.) c. Ball does not land on a number from 6 through 28 The probability of the event that the ball does not land on a number from 6 through 28 is (Type an integer or a simplified fraction.)

To determine the probability that the ball does **not** land on a number from 6 through 28, let's break down the problem step by step. ### Total Slots: - The roulette wheel has **34 slots**: numbers **1 to 32**, plus **0** and **00**. ### Slots to Exclude: - Numbers **6 through 28**: This includes the numbers 6, 7, 8, ..., 28. - **Count of numbers from 6 to 28**: \( 28 - 6 + 1 = 23 \) numbers. ### Slots Not in 6 through 28: 1. **Numbered slots not in 6-28**: - **1 to 5**: 5 numbers. - **29 to 32**: 4 numbers. - **Total numbered slots not in 6-28**: \( 5 + 4 = 9 \) numbers. 2. **Non-numbered slots**: - **0 and 00**: 2 slots. 3. **Total slots not in 6-28**: - \( 9 \) (numbered) \( + 2 \) (non-numbered) \( = 11 \) slots. ### Probability Calculation: - **Total possible outcomes**: **34** slots. - **Favorable outcomes**: **11** slots. \[ \text{Probability} = \frac{\text{Favorable outcomes}}{\text{Total outcomes}} = \frac{11}{34} \] **Answer:** Problem c Answer: The probability is \(\frac{11}{34}\).