A Question in Probability...?

Question

From a well-shuffled standard 52 card deck of playing cards, you pick up the top card, look at it, and place it aside. Then you pick up the next card, look at it, and place it aside. You continue this process. What is the probability that you pick up TWO face cards before ONE ace.

Answer 1

Well, there are only 4 aces, and there are 12 face cards.

So...

52/4 = 13  So, you should pick up an ace about every 13 cards.

52/12 = 4.3  So, theoretically you should pick up 3 face cards before one ace.

Because...

13/4.3 = 3.023

Answer 2

Since the only cards that matter are aces and faces you can pretent the rest of the cards do not exist. That means you have 4 aces and 12 faces.

The odds that the first card you draw is a face card is 12 out of 16, or 3 out of 4. The odds that the second card you draw is a face card is 11 out of 15

that makes the odds of drawing two faces before an ace

(3 / 4) x (11 / 15) = 33 / 60 = 11 / 20 = 0.55 = 55%