Ask Marilyn

Albuquerque Journal - Parade - - ASK MARILYN - by Marilyn vos Sa­vant

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.

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