Question

Two cards are drawn from a fifty-two-card deck. What is the probability that the draw will yield an ace and a face card?

Answer 1

Let me turn the question around and ask you a few questions first:
(1) How many aces are there in a deck of 52 cards?
(2) What is a face card?
(3) How many face cards are there, altogether?
Your answers, if correct, will help you to solve this problem. Good luck!

Answer 2

4 aces

Answer 3

A face card is jack queen and king

Answer 4

12 face cards altogether

Answer 5

That's great; thank you.

Let's look at the original question:

"Two cards are drawn from a fifty-two-card deck. What is the probability that the draw will yield an ace and a face card?"

First of all, what's the P that if you draw one card from a 52-card deck, that that card will be an ACE?

Secondly, what's the P that if you draw one card from a 52-card deck, that that card will be a FACE card?

Answer 6

2/52

Answer 7

BigTime: I'd really like to see your work, not just a possible answer.

First of all, what's the P that if you draw one card from a 52-card deck, that that card will be an ACE? Show your work.

Answer 8

4/52 for your first question

Answer 9

Good.

Secondly, what's the P that if you draw one card from a 52-card deck, that that card will be a FACE card?

Answer 10

Hint:
Bigtim10
A face card is jack queen and king
17 minutes ago
50
Bigtim10 Best Response Medals 0
12 face cards altogether

Answer 11

Secondly, what's the P that if you draw one card from a 52-card deck, that that card will be a FACE card?

Answer 12

Please let me know if you're going to take a break or have something else to do. I'll wait for you, but only for a limited time.

Answer 13

1/52

Answer 14

Yeah I know what a face card is

Answer 15

ok

Answer 16

But you told me there are 12 face cards; how could the probability obtaining a face card now be 1/52?

Answer 17

My mad I read the question

Answer 18

So the P that from a deck of 52 cards, you'll pick a FACE card, is what?

Answer 19

12/52

Answer 20

Very nice.

So: P(ace)m = 4/52 or 1/13, right?
P(face card) = 12/52, or 3/13, right?

Answer 21

yep

Answer 22

OK!
Now we're going to do "sampling with replacement." You'll draw one card, look at it, remember what it is, and then put it back into the deck and shuffle the deck. that way, the P of your obtaining a face card on the second draw is completely independent of whether or not you obtain any particular card on the first draw. Can you agree with that? If not, explain why.

Answer 23

sure

Answer 24

Very sorry for the delay. I lost my internet connection. :(

So, as you say, the P you'll get an ACE on the first draw is 1/13. If you actually draw an ace and then put the card back and shuffle the deck again, and then draw another card, your chances of obtaining a face card are 4/52.

So, P(ace AND face, with replacement, is simply (1/13)(4/52), or (1/13)(1/13)=1/169.

Have you seen any thing like this in class, in your online learning materials, or elsewhere?

Answer 25

no

Answer 26

What we're calculating here is "joint probability:"
It's the probability that on two draws with replacement, the probability
P( Ace AND FACE ) = P(Ace) + P(Face).

Please go back up, find P(Ace) and P(Face) and calculate P(ACE)*(FACE).

Answer 27

The following was already part of our conversation, and thus easily available to you:

P(ace) = 4/52 or 1/13, right?
P(face card) = 12/52, or 3/13, right?

Answer 28

Please go back up, find P(Ace) and P(Face) and calculate P(ACE)*(FACE). Label your result with " P( ACE AND FACE) = " Let me know just how clear (or unclear) this problem is to you at this point.