So, I have a probability related question.
In MTG, which is the probability of landing a 3-drop on turn 3, but using the correct combination. For example, I want to cast a Geist of Saint Traft on turn 3 (assuming I started), what is the probability (given the assumption that I drop 1 land per turn) of having, by turn 3, one island, one plain and one other land and having the card in my hand ready for casting.
I know that as this is drawing without replacement, so some form of Multivariate Hypergeometric Distribution is needed, but I am a little lost.
Let say I have a 60 cards deck: 10 islands, 10 plains, 4 other lands (none of them giving either blue or white mana), 4 Geist of Saint Traft and 32 other cards.
Now, by turn 3 I would have drawn (assuming 1 draw per turn) 9 cards out of the 60 and for dropping the Geist of Saint Traft I would need at least 1 island, at least 1 plain, at least 1 other land (of the other 22 lands) and at least 1 Geist, so in that case would it be the same to calculate the probability of having by turn 3 none of those and subtract that from one? However, I am not sure how to deal with the case of the third land card I should pick it from 22 (the number of lands less the 2 already picked) or from 24 (the total)?