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 (Type an integer or a simplified fraction.)
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To find the probability of the ball landing in a red slot, we first identify the number of red slots. Since there are 32 numbered slots divided equally between red and black, there are 16 red slots. The total number of slots on the roulette wheel is 34. Thus, the probability \( P \) of the ball landing in a red slot is given by the formula: \[ P(\text{Red}) = \frac{\text{Number of Red Slots}}{\text{Total Number of Slots}} = \frac{16}{34} \] Simplifying this fraction gives us: \[ P(\text{Red}) = \frac{8}{17} \] So, the probability of the event that the ball lands in a red slot is \( \frac{8}{17} \).
