Stacking Two Decks

RAY: Let's say you have two ordinary decks of playing cards, minus the jokers. So, you have a deck of 52 cards and another deck of 52 cards. You take them and you shuffle them up--mix them all up as best you can, one hundred four cards.

And then you divide them into two equal piles. So, you've got a pile of 52 on one side of the table, and a pile of 52 on the other side of the table. You have pile A and pile 2.

What are the chances that the number of red cards in pile A equals the number of black cards in pile 2? That's part one of the question. And then part two of the question: how many cards would you have to look at to be certain of your answer?

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[ Car Talk Puzzler ]