Math Is Fun Forum

  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

You are not logged in.

#51 2011-08-18 05:05:40

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Tricky Coin Flipping Probability Problem

Hi;

Lots of languages will handle that.


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.

Offline

#52 2011-08-18 05:22:28

russellhq
Member
Registered: 2011-08-13
Posts: 6

Re: Tricky Coin Flipping Probability Problem

bobbym wrote:

Hi gAr;

I think you found another way to do it.

Possibly he means this:

Left out any simplification that might hide his method. This is what I was looking for, for two days. A formula! No one had it.

I think I understand it, but I am not sure what you are doing here:

How do I calculate this in Excel?

Offline

#53 2011-08-18 05:34:10

gAr
Member
Registered: 2011-01-09
Posts: 3,482

Re: Tricky Coin Flipping Probability Problem

Hi,

Something like this:

BINOMDIST(50,100,.5,0)

I checked in libreoffice, maybe the same in ms excel.

edit: Sorry, this is a probability distribution! See next post.

Last edited by gAr (2011-08-18 05:44:51)


"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."

Offline

#54 2011-08-18 05:37:37

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Tricky Coin Flipping Probability Problem

That is called an NCR or a binomial. It means 100 choose 50. There will be something in excel to do that. Search around for keywords binomial, choose, ncr, combinations.

As a test function when you have found the correct one it will get
an answer of 1.008913445455643 x 10^29.


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.

Offline

#55 2011-08-18 21:33:02

russellhq
Member
Registered: 2011-08-13
Posts: 6

Re: Tricky Coin Flipping Probability Problem

Now the hard work has been done big_smile I wonder if we can expand to a general formula:

If we have a number of events, n, with each event having a probability of success p, and the maximum deviation we want is d.  What would our formula look like (I've had a go but not so sure)?

Last edited by russellhq (2011-08-18 21:34:07)

Offline

#56 2011-08-21 00:24:39

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Tricky Coin Flipping Probability Problem

Hi;

I was able to get the problem down to a 60 x 60 markov chain.
Using that I could get a closed form for this particular problem.

You must enter odd numbers because it is impossible to go broke on
an even number.


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.

Offline

#57 2011-08-21 04:07:28

gAr
Member
Registered: 2011-01-09
Posts: 3,482

Re: Tricky Coin Flipping Probability Problem

Hi bobbym,

That's a nice form.

Where can I read about how to get a closed form from a markov chain?


"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."

Offline

#58 2011-08-21 05:27:38

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Tricky Coin Flipping Probability Problem

Hi gAr;

Nowhere actually but I will explain it as best as I can as soon
as I get something together.


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.

Offline

#59 2011-08-21 07:42:51

gAr
Member
Registered: 2011-01-09
Posts: 3,482

Re: Tricky Coin Flipping Probability Problem

Hi bobbym,

Okay, thanks.

I thought of a recurrence

We may get some insight on the generating function for each dollar from this?


"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."

Offline

#60 2011-08-21 08:59:46

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Tricky Coin Flipping Probability Problem

Hi gAr;

I did not know you were around. Thanks for the recurrence. Unfortunately
Wolfram Alpha will not run the command you need to get that answer.
I do not know of another way or why it is having a 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.

Offline

#61 2011-08-21 15:31:26

gAr
Member
Registered: 2011-01-09
Posts: 3,482

Re: Tricky Coin Flipping Probability Problem

Hi bobbym,

I don't know of a command either for 2 variable recurrence.
I checked that recurrence for small values using a 30x30 table, works fine.

I'll see whether I can get a g.f for that.


"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."

Offline

#62 2011-08-21 15:49:22

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Tricky Coin Flipping Probability Problem

Hi gAr;

Okay, I have been working with shrinking the markov chain down to a small size.
I got it down to 32 x 32 which is much better.


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.

Offline

#63 2011-08-21 15:53:07

gAr
Member
Registered: 2011-01-09
Posts: 3,482

Re: Tricky Coin Flipping Probability Problem

Hi bobbym,

Oh, that's great!
I'd like to see that.


"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."

Offline

#64 2011-08-21 16:06:30

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Tricky Coin Flipping Probability Problem

Hi gAr;

By observing that once you reach + 58 (which will take 43 or more tosses).
There will be 57 or less tosses left. So, upon reaching 58+ there is no way
that you can now go broke.
Therefore we call 58+ an absorbing state because computing
them in no way can effect the prob of going broke.

We can shorten the matrix down further by taking 2 throws
at a time.

For every two tosses.


Raising A to fiftieth power produces the correct answer in
the first row and last column.


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.

Offline

#65 2011-08-21 16:16:51

gAr
Member
Registered: 2011-01-09
Posts: 3,482

Re: Tricky Coin Flipping Probability Problem

Hi,

Okay, I'll see.

And for that recurrence, I think find a generating function may not be easy.
There is an extra condition, we must leave out u[t][0] from adding to the next toss. Otherwise, it's like playing even after going broke.


"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."

Offline

#66 2011-08-21 16:17:43

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Tricky Coin Flipping Probability Problem

Hi gAr;

I am being called away, be back in a couple.


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.

Offline

#67 2011-08-21 16:20:36

gAr
Member
Registered: 2011-01-09
Posts: 3,482

Re: Tricky Coin Flipping Probability Problem

Hi bobbym,

Okay, see you later.


"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."

Offline

#68 2011-08-21 18:13:13

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Tricky Coin Flipping Probability Problem

Hi;

What do you use for the initial conditions?


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.

Offline

#69 2011-08-21 19:27:16

gAr
Member
Registered: 2011-01-09
Posts: 3,482

Re: Tricky Coin Flipping Probability Problem

Hi,

The initial condition is

Maybe we can avoid u(t,0) in the table, since it can be calculated from the other probabilities in that row.
Hence,


"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."

Offline

#70 2011-08-21 21:09:51

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Tricky Coin Flipping Probability Problem

Hi gAr;

Okay, thanks.


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.

Offline

Board footer

Powered by FluxBB