it's been a (long) while since I've taken a math / probability class, so my memory is rather hazy.
Suppose I have a deck of 100 cards, 50 of which are aces, and 50 of which are kings.
How would I model (with some sort of mathematical expression) the probability of drawing (at least) ONE Ace card after N draws, if:
- 1 Card is drawn each time.
- If the card is not an Ace, it is put back (replaced) in the deck (total cards remains 100)
- The deck then has 3 King cards removed and replaced by 3 Ace cards (n + 3 ace cards, n - 3 king cards).
- The deck is then shuffled/randomized.
I thought it might be expressed by some sort of hyper-geometric distribution, but I'm not sure how to go about the "increase the flat chance of success by 3%" (the replacement of the 3 Kings with 3 Aces).