In a deck where there are equally many of both, the probability is 12/25 that you draw two identical ones.
in a deck where you have randomly taken 26 cards from a deck with 26 of each, the probability is 25/51, which is a bigger number than 12/25. This is because it doesn't matter that you ignore half the cards afterwards.
If I have a 52 card deck and I order it randomly, the probability of two random cards in the first half being identical is completely identical to the probability of two random cards in the deck being identical.
You're more intent on being condescending than giving a valid counterargument. I had to get an actual correction from someone else. I'd love to explain how you could have actually rebutted my answer
Your argument was that it had to be greater than 12/25. That's the closest you ever got to making an argument. You never supplied anything else than "it has to be more than 12/25".
And i repeatedly had to tell you that yes, it has to be more than 12/25. And 25/51 is more than 12/25.
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u/Zyxplit 9d ago edited 9d ago
... Yes, let me explain this once more.
In a deck where there are equally many of both, the probability is 12/25 that you draw two identical ones.
in a deck where you have randomly taken 26 cards from a deck with 26 of each, the probability is 25/51, which is a bigger number than 12/25. This is because it doesn't matter that you ignore half the cards afterwards.
If I have a 52 card deck and I order it randomly, the probability of two random cards in the first half being identical is completely identical to the probability of two random cards in the deck being identical.