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 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. v. woun iou nus un on un wu The probability of the event that the ball lands on 31 or 00 is \( \frac{1}{20} \). (Type an integer or a simplified fraction.) c. Ball does not land on a number from 25 through 29 The probability of the event that the ball does not land on a number from 25 through 29 is \( \frac{5}{6} \). (Type an integer or a simplified fraction.)

If you're curious about roulette's historical roots, this casino staple dates back to the 18th century in France, where it was popularized among the elite. The name "roulette" actually means "little wheel" in French, and it was originally envisioned as a form of entertainment for nobles! The modern version we enjoy today evolved through various iterations, blending chance and strategy in an enticing way. For a real-world application, understanding roulette probabilities can enhance your gaming experience! Rather than just throwing down chips randomly, knowing the odds can influence your betting strategy. For example, knowing that the ball has equal chances of landing in any of the 40 slots allows players to compute the likelihood of hitting specific numbers or colors, making for a more calculated approach to placing bets at the table!