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.
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Sure! Let’s dive into the probabilities related to a roulette wheel with 40 slots. (a) **Probability of landing on a red number:** Since there are 18 red slots out of 38 (the 0 and 00 are not red), the probability of the ball landing on a red slot is calculated as follows: P(Red) = Number of Red Slots / Total Slots = 18 / 40 = 0.45 or 45%. (b) **Probability of landing on a black number:** Similarly, there are also 18 black slots. The calculation is the same: P(Black) = Number of Black Slots / Total Slots = 18 / 40 = 0.45 or 45%. (c) **Probability of landing on a green number (0 or 00):** There are 2 green slots, so: P(Green) = Number of Green Slots / Total Slots = 2 / 40 = 0.05 or 5%. (d) **Probability of landing on an odd number:** There are 19 odd numbers from 1 to 38. Therefore, the probability is: P(Odd) = Number of Odd Numbers / Total Slots = 19 / 40 = 0.475 or 47.5%. So, the probabilities for each event have been calculated based on the distribution of the slots!