The reason the math doesn’t work is that the two events are not independent. Hyper geometric distribution calculators (online one) only work when you ask a simpler question, like the odds of at least one land in a 7 card hand. As soon as you ask a more complicated question, you need to think in terms of combinations instead. What you want here, depends on what you are asking.
For example, do you mean exactly one of each? At least one of each? Percent chance of getting at least one but not the other?
Unfortunately, each one has slightly different calculations.
The basic form can be found here:
http://birdsofparadise-mtg.blogspot.com ... etric.htmlFor your question, I think you want (8 choose 1)*(8 choose 0)*(24 choose 6)/(40 choose 7)
Let me englishify this for you: the first term is how many ways we can pick one mountain from 8, next is how many ways to get 0 swamps from 8 (slightly tricky concept, but the answer is just 1 by definition*), then how many ways can the rest of the deck be ordered (huge number here), divided by how many ways can the whole deck be ordered (even bigger number).
Why the number choices? 8 land one mountain, 8 lands no swamps, 24 remaining cards (40-16 lands) with 6 chosen (doesn’t matter which), 40 and 7 just are deck size and hand size.
The problem is that your question is more complicated. Depending on what you specifically want to ask, you may need to sum across multiple calculated probabilities (for the at least one, I think we need to sum 8 calculations, but I need to think about it). That said, I think I figured out an easier way to do this last time I looked at it, let me think on it, and I’ll share it when I remember.
*complex mathematical proof is not needed, but it exists, in case you ever feel like going full nerd.