During a card game, I said that the probability of getting dealt two aces is the same as getting an ace and a deuce—that the chance of getting any two cards is the same, whatever they are. My friends say I’m wrong. Who’s right?
—Richard Day, Pelham, Ala. Your friends are right. To illustrate, let’s narrow the question to the red or black half of the deck with only two aces and deuces. Lay the four cards in a grid—aces on the left and deuces on the right, like this: To get two aces, you must be dealt the left column. (And to get two deuces, you must be dealt the right column.) But to get one ace and one deuce, you can be dealt either the top row or the bottom row. So getting one of each is more likely.