I'm generally good with math, but probability calculation just seems to fight me.
I'm trying to develop a formula to determine the odds of hitting at least 2 spades, given that the player is dealt their first 3 cards.
The probability is about 15.05%. I have confirmed this by running 5 million simulated 3 card hands and comparing how many times 2 or 3 spades hit. This is agrees with the online calculator here: https://www.ohrt.com/odds/index.php?t=52&d=3&o=13&c=2&&s=any&p=9
By my reasoning, the formula to arrive at the probability should be:
or "from 13 spades, take 2, from the remaining cards, take 1, and divide by the total number of 3 card combinations in a 52 card deck".
But that gives me a result of 17.65%.
I'm trying to develop a general formula for any number of outs or cards dealt(similar to the online calculator), but this was the test case I've been stuck on for a while.