How do you calculate the probability of drawing two face cards without replacement?

To calculate the probability of drawing two face cards without replacement, multiply the probabilities of each draw.

First, let's understand what face cards are. In a standard deck of 52 playing cards, face cards are the Jacks, Queens, and Kings. There are 3 face cards in each of the 4 suits (hearts, diamonds, clubs, and spades), making a total of 12 face cards.

When drawing cards without replacement, the total number of cards in the deck decreases with each draw. For the first draw, the probability of picking a face card is the number of face cards divided by the total number of cards. So, the probability of drawing a face card first is 12/52.

If you successfully draw a face card on the first draw, there are now 11 face cards left and only 51 cards remaining in the deck. The probability of drawing a face card on the second draw is then 11/51.

To find the overall probability of both events happening (drawing a face card first and then another face card), you multiply the probabilities of each individual event. Therefore, the probability is (12/52) * (11/51).

Simplifying this, you get:

(12/52) * (11/51) = (3/13) * (11/51) = 33/663 = 1/20.

So, the probability of drawing two face cards in a row without replacement is 1/20, or 5%.