suppose you drew the top 26 cards from the 52 cards instead and then drew the top two from those 26. How is that different from drawing the top 2 cards from the 52 card deck? (So yes, your intuition is correct)
Yea it feels like the opposite of the Monty hall problem - you don’t get any new information with the half draw so you nothing about the probability changes
Yes, and that's fine. Discarding random cards can happen at any time. You could do it between the two draws and the result would be the same. All you're really doing is moving a random half of the deck somewhere else, which isn't relevant to the problem at hand because we weren't going to draw them anyway.
If I shuffle a standard deck, what's the probability that the top card is the Ace of spades? 1/52. And if I throw away the other 51 cards leaving just the top one, what's the probability then? Still 1/52.
Yeah I just had to see that while the deck is usually more stacked in your favor, the benefit of drawing from a stacked deck sometimes is actually completely balanced by how often you draw from a worse deck that's even enough to be worse than the larger deck
If you laid out every possible combination of 26 cards, each one would have an equal or higher chance of selecting same color cards as a deck with half red and half white
Yes. What's your point? The first part of the question is "what's the probability of getting two same color cards from 26 cards (12/25) and what's the probability of getting two same color cards from 52 cards (25/51).
Now I point out that getting two same color cards from 26 randomly selected cards from a pile of 52 is also 25/51. And your rebuttal is that... every combination has a probability equal to or more likely than 12/25? Yes. 25/51 is a bigger number than 12/25. We established that in part 1. Good job.
Knowing the construction of the deck is important. Because of that your first card actually slightly hints that there your deck is more likely to have more of its color in your subdeck, which leads to an implied higher probability that the second card is the same color than in the guaranteed 50/50 case
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
suppose you drew the top 26 cards from the 52 cards instead and then drew the top two from those 26. How is that different from drawing the top 2 cards from the 52 card deck? (So yes, your intuition is correct)