You have a 4-card deck containing a king, a queen, a jack, and a 10. You pick a card, keep it, and then pick another card. What is the probability that you pick exactly 1 face card?
(Face cards are jacks, queens,and kings.)

Please give an explanation.

Question

You have a 4-card deck containing a king, a queen, a jack, and a 10. You pick a card, keep it, and then pick another card. What is the probability that you pick exactly 1 face card?
(Face cards are jacks, queens,and kings.)

Please give an explanation.

jhannybean · Answer

@nincompoop

anonymous · Answer

what?

jhannybean · Answer

I am ressurecting him to assist you with your question~ Rise my minion!

anonymous · Answer

oh

jhannybean · Answer

Tbh I am horrible at stats,or rather, probability related questions.

anonymous · Answer

i just really need the explanation. i have the answer its just that i am confused on how the question is worded

anonymous · Answer

thanks for trying though

nincompoop · Answer

@waterineyes please help

nincompoop · Answer

I thought I'd learn the mathematical way from one of the best LOL

anonymous · Answer

Don't know really but let me give a try.

If you pick 10 at first, then probability of face cards will be 1/3..

And if you pick one face card on first try, then probability of other face card will be 1/2.

And if you pick face card on first try, then 10 at other then, no probability.. :)

Don't know actually, and I don't want to misguide the asker..

nincompoop · Answer

LMAO! 
I was thinking with four cards, there's 3 out of 4 chances;
but since we picked an unknown card, and left with 3 with the following possibilities: 3 face cards, which will give us 1 out 3 chances of getting a face;2 face cards and a 10 will give us 1 out of 3 or 2 out of 3.  Now, I am stuck in putting this in mathematical equation or composition.

nincompoop · Answer

@KingGeorge I have a feeling that the new graduate will not upset us :D

kinggeorge · Answer

I would naturally think about this more in the way that waterineyes thought about it. Basically, you have two ways to do it.

Case 1: You choose the 10 first. Then anything else you draw afterwards will be a face card. The probability of this happening is 1/4 (chance to draw the 10).

Case 2: You choose something else first, and then the 10. This has a (3/4)*(1/3)=3/12 chance of happening.

So the total probability is (3/12)+(1/4)=1/2

There is another method that I like as well.

kinggeorge · Answer

The other method would be to look at all the possible two card hands you draw. There are $\binom{4}{2}=6$ ways to choose 2 cards. How many of these have the 10? 

Well, we have to have the 10, so we have three remaining cards left to choose one card from. So $\binom{3}{1}=3$. Hence, the probability is 3/6=1/2.

kinggeorge · Answer

Did at least one of these methods make sense?

nincompoop · Answer

the second answer you gave made more sense to me. it cuts through the minute details.

kinggeorge · Answer

It certainly is a bit more elegant. But I think the first one is the more "obvious" way to do it, and perhaps a bit easier to understand.

nincompoop · Answer

agreeable. the second one is more systematically, which also a bit easier for me to understand and translate to higher magnitude or complexity.

kinggeorge · Answer

Agreed. It's much easier to generalize the second one to more difficult problems.