I'm playing a card game where you begin with 5 cards and if you mulligan, you place them at the bottom and draw 5 new cards. If I were to use a standard 52 poker deck what I'd be asking is:
What is the probability to draw at least 2 diamond cards if I mulligan on a failure?
Keep in mind on mulligan we have known information. If we hit 0 or 1 diamonds, they would go to the bottom giving use 2 possible mulligan scenarios. I'm looking for a formula so I can apply it to a card game to determine the amount of a card type to include to reach a 90% success rate of this scenario.