Question

What is the probability of the following situation:

Two face cards are drawn in a raw (WITHOUT REPLACEMENT) from a standard deck of 52 playing cards given that the first card is drawn is a king?

Answer 1

We want to know the probability that a face card is drawn, then another face card is drawn, GIVEN that the first card drawn is a king., we want to know the probability that a face card is drawn, then another face card is drawn, GIVEN that the first card drawn is a king. First off, is a king a face card?

Answer 2

yeah

Answer 3

Right! Face cards are kings, queens, and jacks.
Now how many face cards are there in a 52-card deck?

Answer 4

12 cards

Answer 5

probability that a face card is drawn \(\Large \frac{12C2}{52C2}\)

Answer 6

I'm not going to try to simplify that that (12 choose 2) over (52 choose 2), though it *might* give us the correct final answer, it is not really the method we should use here. Our solution method is much simpler and does not require combinations or permutations.

Answer 7

\(\sf P(face\ card\ drawn| king\ is\ drawn)=\frac{P(face\ card\ and\ king)}{P(king\ is\ drawn)}\)

Answer 8

There are 11 face cards in a a remaining 51 card deck.
What is that probability?

Answer 9

11 out of 51 is the fraction ______?

Answer 10

11/51? then?

Answer 11

I will try to simplify that "(12 choose 2) over (52 choose 2)" you mentioned to see if it gives us the same fraction, but that seems to be an overly complicated way to go about this...

Answer 12

wait, don't tell me this is the answer already? O.o

Answer 13

12 choose 2) over (52 choose 2) does not work. That gives us (12 * 11)/(52 * 51) and we want just 11/51 ..... I think I see where you get that formula from though.
IF we did NOT know what the first card was.... If we wanted to know what the probability of drawing a face card, then another face card, without probability, then the answer would be:

Probability of drawing a face card the first card: 12/52 (there are 12 face cards in 52 cards)

probability of drawing a face card the second time without replacement: 11/51 (there are 11 face cards in 51 cards)

= (12 * 11)/(52 * 51)
Which is what "(12 choose 2) over (52 choose 2)" eventually simplifies to.

Though just calculating the individual probabilities (12/52 and 11/51) and then multiplying them is a much easier way to go about it. However that all is only if you do NOT know what the first draw is.

In our problem, we are given that the first draw is a king.
So we know that the first card was a face card and the probability of the first draw being a face card is 100%, or just 1. Then the total probability of both events happening is not:

(12/52)(11/51)
but instead:
(1)(11/51)
So the probability is just 11/51 :^)

Answer 14

hmm.. that makes sense..
that's what i think before BUT the correct answer is 11/663 and I don't have any idea where did they get 663 from

Answer 15

Me neither. 11/51 should be correct.

To check, this is the complete set of instructions? :
''What is the probability of the following situation: Two face cards are drawn in a row (WITHOUT REPLACEMENT) from a standard deck of 52 playing cards given that the first card is drawn is a king?''

Answer 16

663 is 3*13*17, and I cannot figure out where any of those numbers could have come from.

Answer 17

yeah..
here.. letter e

Answer 18

Okay, I see it. 11/51 is the correct final answer. If it says something else then there must be an error in the computer system.

Answer 19

And there is no different formula, this problem is just that there are 11 face cards in 51 total cards, so the probability of drawing a face card is only 11/51. No extra formula or calculation needed, it really is that simple.

Answer 20

i knew it >.> error in the book and they don't believe me, smh
i spent my 4 hours just trying to figure this one out

thanks for the help :)

Answer 21

You may want to ask your teacher about this since there is an error in the system somewhere.

Answer 22

Haha, I knew it too. :^)

Answer 23

i'm just helping someone in this homework , i'll just tell her to ask her teacher lol

Answer 24

Alright, good luck!