They're not independent. (At least the last time I played,) they pull prizes out of the pool when you win them. So if there is 1 Peach in a 100-prize pipe, at most you have to buy 100.
Source? I searched around and the first source[1] seems to confirm what you say
>you can only receive a certain number of rewards from each rarity level per 100 Pipe uses
but further down it says
>Additionally, as long as you haven’t exhausted the quantity by rarity for its category, you can receive duplicates of a reward from the Pipe.
However, it also says
>In fact, you’re guaranteed to receive at least one reward of each type by the time you’ve used 100 Pipe pulls — though the exact reward you’ll get is random for all categories except High-End Spotlight.
I agree that each roll isn't independent and you can't model it as such, but I don't think there's any mechanism to guarantee you a prize given enough rolls, and I still suspect the author messed up the math.
>you can only receive a certain number of rewards from each rarity level per 100 Pipe uses
but further down it says
>Additionally, as long as you haven’t exhausted the quantity by rarity for its category, you can receive duplicates of a reward from the Pipe.
However, it also says
>In fact, you’re guaranteed to receive at least one reward of each type by the time you’ve used 100 Pipe pulls — though the exact reward you’ll get is random for all categories except High-End Spotlight.
I agree that each roll isn't independent and you can't model it as such, but I don't think there's any mechanism to guarantee you a prize given enough rolls, and I still suspect the author messed up the math.
[1] https://www.gamerevolution.com/guides/600991-mario-kart-tour...