Math Is Fun Forum

chineseballer06

Member

Registered: 2011-02-01

Posts: 34

Probability

Stuck on this problem.  Any help is appreciated

What is the probability that in a player's hand of 13 cards at least one suit will be missing? 

I'm assuming that this is from a standard deck of cards.

soroban

Member

Registered: 2007-03-09

Posts: 452

Re: Probability

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bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Probability

Hi guys;

There is a problem with that solution.

Maybe there a is typo in your answer, please check it.

I think the problem has to be done using the principle of inclusion exclusion.

I am getting:

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Probability

Hi all,

bobbym,

Did you do it case by case?
Will this work : P(atleast 1 suit missing) = 1 - P(none of the suits are missing) ?

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Probability

Hi gAr;

I did it by partitions and then the multivariate hypergeometric distribution. It is too long for a post and I am working on a shorter solution.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Probability

Hi bobbym,

What I did was a simple mistake in my program, I was adding instead of multiplying.
I took partitions of length 4. Then steps involving permutation of that partition (is this what you called multivariate hypergeometric distribution?)

Required Probability =  1 - 602586261420/52C13,
1−30129313071/31750677980 ≈ 0.0510655208692334, slightly less than your answer!

Last edited by gAr (2011-02-05 02:28:03)

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Probability

Hi;

Found the answer, first answer slightly incorrect because it was too long, I made a typo on it. Here is a better answer.

Wait , hold the presses, my brother answered this in under a minute. When I asked how??????? He said to me, "look here dummy."

http://www.math.uiuc.edu/~laugesen/461/ … 2006f.pdf.

Question 3b.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Probability

Hi,

The answer is neat, but I'm trying to understand!

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Probability

Hi;

The method is the principle of inclusion and exclusion. If you have seen Venn diagrams, derangement problems or rook polynomials then you have been exposed to it.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Probability

Yes, I know those, but got confused with this particular problem.

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Probability

Hi;

So did everybody else who looked at it.

For your earlier question of the Multivariate hypergeometric distribution. Please go here, my post prob 4)

http://www.mathisfunforum.com/viewtopic … 34#p119834

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Probability

Hi,

It's interesting!

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

chineseballer06

Member

Registered: 2011-02-01

Posts: 34

Re: Probability

Hey every one yeah I think bobbym has the right approach because that was the answer in the back and we have just started to learn about the inclusion exclusion principle.  Thanks to everyone for their inputs it really helped!

chineseballer06

Member

Registered: 2011-02-01

Posts: 34

Re: Probability

I was just curious does anyone know how to do this problem in the way that gAr suggested?

By doing 1 - P(none of the suits are missing)?

chineseballer06

Member

Registered: 2011-02-01

Posts: 34

Re: Probability

Sorry Bobbym,

I'm a little confused about how to use the inclusion exclusion principle.  What are my 3 events that I am taking the union of?

chineseballer06

Member

Registered: 2011-02-01

Posts: 34

Re: Probability

That link that you sent in box #7 doesn't seem to be working for me

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Probability

Hi chineseballer06;

Right click the link and "Save link as" to download the pdf.

I would not start on that problem if I was just learning the P.I.E.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

chineseballer06

Member

Registered: 2011-02-01

Posts: 34

Re: Probability

Hi bobbym,

Its still not working for some reason, it says the page has been removed.  And I've already learned it thats just the topic we finished in class so that is probably how my professor wants me to solve this problem

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Probability

Hi;

You do not view it as a page you download it as a pdf. Which adobe or some other reader can read

Right click the link and click "save link as" from the menu?

I have just downloaded it again.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

gAr

Member

Registered: 2011-01-09

Posts: 3,482

Re: Probability

Hi all,

chineseballer06,

You could not download because hyperlink reads

http://www.math.uiuc.edu/~laugesen/461/test1soln_2006f.pdf.

Notice the dot at the end.
The actual location is without a dot at the end.

---

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

chineseballer06

Member

Registered: 2011-02-01

Posts: 34

Re: Probability

Got it!
Thanks everyone!

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Probability

Hi chineseballer06;

Your welcome. It was a nice problem.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.