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 (Type an integer or a simplified fraction.)

To find the probability of landing on 0 or 32, we need to consider how many favorable outcomes there are and the total possible outcomes. In this case, there are 2 favorable outcomes (the slots 0 and 32) out of a total of 34 slots. So, the probability that the ball lands on 0 or 32 is given by: \[ P(0 \text{ or } 32) = \frac{2}{34} = \frac{1}{17} \] Now, let's add a little historical flair! Roulette has roots back to 18th century France, deriving its name from the French word meaning "little wheel." Originally created as a simple gambling game, it quickly evolved into a casino classic that has captured the hearts of many players worldwide. The iconic spinning wheel is now a symbol of chance, luck, and a sprinkle of excitement! And to keep the fun rolling, did you know that there are various strategies players use to try to beat the odds? Some swear by the Martingale system, doubling bets after losses, while others opt for the Fibonacci strategy, betting based on a sequence of numbers. Remember, no strategy can change the probabilities—always play responsibly!