Math Is Fun Forum / Is this cool with you?

gAr · 2012-06-24 22:01:57

Hi,

You're welcome.

bobbym · 2012-06-24 22:05:15

Hi gAr;

Have you seen juans last problem?

gAr · 2012-06-24 22:27:23

Which one, finding miinimum value?

bobbym · 2012-06-24 22:30:18

Hi;

Sorry, did not see he posted some after that. Take a look at this one. I solved it but in an unconvincing way.

http://www.mathisfunforum.com/viewtopic.php?id=17797

gAr · 2012-06-24 22:34:05

Okay, I'll see that and post there if I have anything to say...

bobbym · 2012-06-24 22:39:19

Thanks, that would be good. My answer is in post #33 of that thread.

bobbym · 2012-07-12 07:30:06

New Problem:

A and C are asked at their new job to tackle a problem. The casino would like to know what the expected difference is of the total of the first and the total of the second die if a pair are thrown 123456787654321 times. For example if a pair are thrown 3 times (3,6), (5,4), (1,1) the sum of the first die is 3+5+1=9 and the sum of the second die is 6+4+1=11 the difference is 2.

A instructs C to run a simulation assuring him that no mathematical solution is possible. He claims that his vast knowledge of meromorphic functions proves this. C believes him and runs a large simulation that takes 3 days of computer time.

The supervisor of the computing division is outraged at the 3 days usage and asks C for an explanation. C explains that he was correct and A agrees. The supervisor immediately fires A and C.

A and C immediately run back to B complaining about the supervisors treatment. B starts to laugh at their misfortune,

B says) You two turkeys really are overcooked. Of course there was a simple mathematical solution. You wasted 3 days on a giant mainframe and should be fired.

A says) Hold on B, I have had enough of your insolence. My mathematical knowledge dwarfs yours and that supervisor's too. I am right and we were fired unjustly.

D says) Here, here! A you are truly a champion of justice and mathematics too.

E says)A is a dullard and C is even worse for believing him!

Is A being fired cool with you? Is B right that they wasted the casino's money?

anonimnystefy · 2012-07-12 10:07:24

Hi bobbym

anonimnystefy · 2012-07-12 10:35:21

bobbym wrote:
This prob came up somewhere else:

A coin with probability p of heads is tossed until a head appears for the first time. If the probability that the number of tosses required is {2,4,6,8,10...} is 2/5, then find p:

B solves it like this:

The chance that a head comes up on an even toss is:

Now sum that series:

Set the sum to 2/5 and solve for p.

Solve the equation any way you can, to get p = 1/3

Has B solved the problem?

Of course she has!

gAr · 2012-07-12 17:10:46

Hi bobbym,

Last edited by gAr (2012-07-12 17:13:52)

bobbym · 2012-07-12 20:09:41

Hi gAr;

gAr · 2012-07-12 20:37:18

Hi bobbym,

bobbym · 2012-07-12 20:44:01

Hi gAr;

gAr · 2012-07-12 20:53:59

Hi,

bobbym · 2012-07-12 21:03:55

Hi gAr;

gAr · 2012-07-12 21:19:28

Hi,

I think we are not doing the same thing.

Suppose we throw the dice 4 times, (1,4), (5,3), (5,6), (2,3), we are taking absolute value of the difference? |(1+5+5+2)-(4+3+6+3)| = |13-16| = 3
Are we estimating the difference like that on the long run?

bobbym · 2012-07-12 21:30:20

Yes, that is what my example indicates. When I see a nice solution I get too excited and rush to post it. This has hurt me before and I must learn to slow down. To post it when I am sure I understand what was shown to me.

If we add the numbers like that the difference will approach zero. The expected value of both die will be 3.5.

I did not show the correct way to subtract the die!

(3,6) = 3
(5,1) = 4
(3,3) = 0
(5,6) = 1

(3+4+0+1) = 8

That is the correct way. Pairwise!

gAr · 2012-07-12 21:46:24

bobbym · 2012-07-12 21:58:57

Hi;

gAr · 2012-07-12 22:11:45

Hi bobbym,

Last edited by gAr (2012-07-12 22:15:04)

bobbym · 2012-07-12 22:13:43

Hi;

gAr · 2012-07-12 22:17:32

Hi,

But we are considering abasolute values, it must be increasing, isn't it?

bobbym · 2012-07-12 22:22:05

Hi;

I am pretty sure even with the absolute value the expected difference between 2 die can never be more than 5. (6,1) being the maximum. That is what this guys formula indicates. If I am wrong here it is because I did not present the problem correctly.

gAr · 2012-07-12 22:31:00

Yeah, the way I understand the problem leads me nowhere else.
Perhaps you could post a code in procedural manner for simulation, so that I may understand the actual question?

bobbym · 2012-07-12 22:36:57

Hi gAr;

Okay, let's put into a form that we both agree on and gets the same answer he got. Do not worry I will send you the page when we are done so you can see what Robert Israel did without my interpretation getting in the way.

Here is the algorithm:

1)Pick two random integers in the interval [1,6].
2)Subtract them and take the absolute value.
3)Take the average of all of those values.
4) Print the answer.

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#1451 2012-06-24 22:01:57

Re: Is this cool with you?

#1452 2012-06-24 22:05:15

Re: Is this cool with you?

#1453 2012-06-24 22:27:23

Re: Is this cool with you?

#1454 2012-06-24 22:30:18

Re: Is this cool with you?

#1455 2012-06-24 22:34:05

Re: Is this cool with you?

#1456 2012-06-24 22:39:19

Re: Is this cool with you?

#1457 2012-07-12 07:30:06

Re: Is this cool with you?

#1458 2012-07-12 10:07:24

Re: Is this cool with you?

#1459 2012-07-12 10:35:21

Re: Is this cool with you?

bobbym wrote:

#1460 2012-07-12 17:10:46

Re: Is this cool with you?

#1461 2012-07-12 20:09:41

Re: Is this cool with you?

#1462 2012-07-12 20:37:18

Re: Is this cool with you?

#1463 2012-07-12 20:44:01

Re: Is this cool with you?

#1464 2012-07-12 20:53:59

Re: Is this cool with you?

#1465 2012-07-12 21:03:55

Re: Is this cool with you?

#1466 2012-07-12 21:19:28

Re: Is this cool with you?

#1467 2012-07-12 21:30:20

Re: Is this cool with you?

#1468 2012-07-12 21:46:24

Re: Is this cool with you?

#1469 2012-07-12 21:58:57

Re: Is this cool with you?

#1470 2012-07-12 22:11:45

Re: Is this cool with you?

#1471 2012-07-12 22:13:43

Re: Is this cool with you?

#1472 2012-07-12 22:17:32

Re: Is this cool with you?

#1473 2012-07-12 22:22:05

Re: Is this cool with you?

#1474 2012-07-12 22:31:00

Re: Is this cool with you?

#1475 2012-07-12 22:36:57

Re: Is this cool with you?

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