Question

Need Help with Probability Question: You are planning to draw 2 cards at random (from a standard 52 card playing deck) without replacement. Your goal is to pull out a face card on the first draw and a diamond on the second draw. Let suppose that you have a roll of quarters with one special quarter somewhere in the roll......

Answer 1

Here's the full question:

You are planning to draw 2 cards at random (from a standard 52 card playing deck) without replacement. Your goal is to pull out a face card on the first draw and a diamond on the second draw.
Let suppose that you have a roll of quarters with one special quarter somewhere in the roll. As the roll of quarters gets bigger, your probability decreases. How many quarters would you need for the probability of selecting the special quarter to be the same as the probability of pulling out a face card on the first draw and a heart in the second draw without replacement?

Answer 2

Ok, so you want to find the probablity of selecting those cards, we can do that and let's worry about quarters later.

What's the probability of getting a face card on the first draw?

Answer 3

There's 12 face cards so ..12/52=0.23?

Answer 4

right, the problem here is that you draw the two cards without replacement, so that makes them dependent.
I would calculate the probability of drawing a heart face card on the first draw and any heart on the second, and also the probability of getting a non-heart face card on the first draw and a heart on the second.
If you add these two probabilities together, do you see that we get the probability that we're after?

Answer 5

Ok..{bear with me I'm not that great at this} .If I draw a heart faced card on the 1st draw and any heart on the 2nd then I would have--> (3/52)(12/51)=.01. If I draw a non-heart face on the 1st and a heart on the second then I would have--> (49/52)(13/51)=.24. If I add the two probabilities together then I should get--> .01+.24=.25?

Answer 6

You're right, but you've misunderstood me. By a non-heart face card I meant a face card of clubs, diamonds or spades. So that probability is (9/52)(13/51)=0.04.

adding them together and we get 0.05

This works because if you draw a face card first, it's either of hearts, or not. So when we calculate both probabilities and add them together we get what we want.

Answer 7

My first idea was to just calculate the probability of getting a face card on the first draw, but that doesn't work because then you don't know how many hearts are left in the deck.

Answer 8

I hope it makes sense, otherwise be sure to ask.

Answer 9

Yes it's making sense so far. So with the work that we first did, part one is now complete?

Answer 10

yes, let's talk quarters.

So let's say we have n quarters and we want the probability of picking a specific one to be equal to 0.05=1/20.

(we did some rounding earlier, so it's not going to be exact)

Answer 11

What's the probability of picking the special quarter in terms of n?

Answer 12

I'm sorry, where did 1/20 come from?

Answer 13

0.05=1/20

It'll prove easier to write it this way.

Answer 14

is it because .25*20=5?

Answer 15

I suppose, but just type 1/20 into your calculator, you'll get 0.05

Answer 16

Ok. I'm following now.

Answer 17

I'm a bit confused on the probability of picking the special quarter in terms of n...wouldn't it be the same (1/20)?

Answer 18

Yes, in this case, but I what would it be for a more general case?

So the answer to that is some expression with n, which you can then equate to 1/20. From that equation you can then find n, the number of quaters.

Answer 19

I think i'm confused...So for this problem, there is a 1/20 chance that I will pick the special quarter. That being said, n=20 (19 regular quarters and 1 special one)?

Answer 20

I guess I'm making this harder than it is, yes n=20, this was my idea to obtain it:

In general the probability of picking one specific quarter from n quarters in 1/n.

We want this to be equal to 1/20, so 1/n=1/20 -> n=20

Answer 21

Ok. I understand now.

Answer 22

great

Answer 23

and that would be it for part 2 right? Since the probability of pulling a face card then a heart card is equal to .05, the number of quarters that we would need to equal that probability would be 20, which we got from finding that probability through the process we just went through.

Answer 24

That's right, as I've sais we did some rounding, so it might not be exactly 0.05 or exactly 20.

Answer 25

Awesome! Thank you so so much! you've been a great help :)

Answer 26

Thanks, you're welcome.