If you draw 2 cards from a standard 52 card deck without replacement, what is the probability you will draw a face card followed by non-face card?

Question

We can start with what we know and proceed from there. We have a 52-card deck. So, all our total possible outcomes will come from that deck of 52 cards. Our sample space is 52.

We know we have 12 face cards.

We know the remaining cards are nonface cards. We have 40 non face cards.

Answer 1

The probability of getting a face card on draw the first draw is 12/52. Since we do not replace the face card we will have 1 less card in the deck. The probability of getting a nonface card on the second draw is 40/51. 40 because there are 40 nonface cards and 51 because we did not replace our card after we drew it the first time. Then we multiply these two probabilities. 12/52 * 40/51 = 480/2652. If we simplify, we will get 40/221.