May 29, 2021
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.
Same color? The backs of them are red. And the other sides, the business sides are the same. So you take them and you shuffle them up--mix them all up as best you can.
Both decks together, so 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. Are you with me so far?
So, I've shuffled 104 cards together, and I've split them back into two piles of 52 each, and I've got one pile here on my left, and one pile to my right.
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?
The chances are: One hundred percent!
Imagine if you - let's say by some luck, you shuffled up all these cards and all the red cards wound up in one pile, we'll call that pile A. And for simplicity's sake, we'll call the other pile, pile B, and all the black cards wound up in that. Then you would say, well, certainly the number of red cards in deck A, or pile A, equals the number of black cards in pile B. Now, I ask you to construct a scenario where it wouldn't be the case, always.
How about one and 51? Take a card out of pile A and donate it to pile B--but when you do that, you must reciprocate and take a black card from pile B and donate it to pile A. Therefore you have 51 and one, and 51 and one, and no matter how you do this if you wind up with 52 cards in each pile the number red cards in pile A will equal the number of black cards in pile 2.
And part B of the question: How many cards do you have to look at to verify your answer?
You think it's great because you got the answer. If you hadn't gotten the answer, you'd be all over this thing.