Two bottles are drawn with replacement from a crate containing 8 coke, 12 and 4 sprite bottles. What is the probability that the first is coke and the secon...

There are three types of bottles in the crate: Coke, Sprite, and not Coke (which includes Sprite bottles). To find the probability that the first bottle is Coke and the second bottle is not Coke, we need to multiply two probabilities: the probability of selecting a Coke bottle first and the probability of selecting a not Coke bottle (i.e., a Sprite bottle) second. The probability of selecting a Coke bottle first is 8/24 because there are 8 Coke bottles in the crate out of a total of 24 bottles (8 Coke + 12 Sprite + 4 Sprite = 24). After selecting the first bottle, there will be 23 bottles left in the crate. If the first bottle was a Coke bottle, then there will be 7 Coke bottles and 12 Sprite bottles left in the crate. Therefore, the probability of selecting a not Coke (i.e., a Sprite) bottle second is 12/23. Multiplying these probabilities, we get: (8/24) * (12/23) = 96/552 ≈ 0.174 Therefore, the probability that the first bottle is Coke and the second bottle is not Coke is approximately 0.174, which is closest to option (C) 2/9.