You and a friend each randomly draw a card from a standard deck. What is the probability that at least one of you is holding a face card (jack, queen, or king)?

Question

anonymous · Answer

It's the chance that you and your friend draw exactly one face card

plus

the chance that you and your friend both draw face cards

anonymous · Answer

So can you help me cause im still confused

anonymous · Answer

We'll start by calculating the chance that you both draw face cards. The first time, there are 12 face cards and 52 total cards. You have a 12/52 chance of drawing a face card. Now the next person draws. They have a 11/51 chance of drawing a face card. Multiply these together.$$\frac{12}{52}*\frac{11}{51}$$

anonymous · Answer

The next case we consider is when both of you draw, you get exactly one face card. Not zero face cards, and also not two face cards.

anonymous · Answer

You can further break this down. There will be a case where you get the face card and your friend doesn't. There will also be a case where you do not get the face card and your friend does.

anonymous · Answer

When you get the face card and your friend doesn't, the probability is $$\frac{12}{52}*\frac{40}{51}$$

When your friend gets the face card and you don't, the probability is $$\frac{40}{52}*\frac{12}{51}$$

anonymous · Answer

Add these probabilities together:$$\frac{12}{52}*\frac{11}{51} + \frac{12}{52}*\frac{40}{51} +\frac{40}{52}*\frac{12}{51}$$