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 \( \frac{11}{34} \). (Type an integer or a simplified fraction.) d. Ball lands on an odd number or on a green slot The probability of the event that the ball lands on an odd number or on a green slot is (Type an integer or a simplified fraction.)

To find the probability of the events listed, let's break down the information we know: a. For the red slots, there are 16 red slots (half of 32). Therefore, the probability that the ball lands in a red slot is \( \frac{16}{34} = \frac{8}{17} \). b. For the event that the ball lands on 0 or 32, there are 2 favorable outcomes (0 and 32) out of 34 total slots. Thus, the probability is \( \frac{2}{34} = \frac{1}{17} \). c. The numbers from 6 through 28 are \( 6, 7, 8, \ldots, 28 \), which includes 23 numbers. Therefore, the numbers not in this range are \( 0, 1, 2, 3, 4, 5, 29, 30, 31, 32, 00 \), amounting to 11 numbers. The probability of not landing on a number from 6 through 28 is \( \frac{11}{34} \). d. To find the probability of landing on an odd number or a green slot: - The odd numbers from 1 to 32: \( 1, 3, 5, 7, ..., 31 \), which gives us 16 odd numbers. - We also have the two green slots: \( 0 \) and \( 00 \). Now, let's count: - Odd numbers = 16 - Green slots = 2 - There is no overlap between these two sets, so we can simply add them. Total favorable outcomes = 16 (odd numbers) + 2 (green) = 18. Thus, the probability of landing on an odd number or green is: \[ \frac{18}{34} = \frac{9}{17} \] Summarizing: a. Ball lands in a red slot: \( \frac{8}{17} \) b. Ball lands on 0 or 32: \( \frac{1}{17} \) c. Ball does not land on a number from 6 through 28: \( \frac{11}{34} \) d. Ball lands on an odd number or on a green slot: \( \frac{9}{17} \)