Is this cool with you?

bobbym · 2011-05-04 00:24:40

Not really, I missed that! You know what, not even the packages could find that factorization.

bobbym · 2011-05-26 08:38:24

New Problem:

A deck of cards are dealt out in a circle. What is the expected number of pairs of adjacent cards which are both red?
A says) 25 / 2.
B says) Nope!
C says) It is more like 51 / 4.
D says) I once shuffled a deck and when I spread them they were all r,b,r,b,r,b etc. Anyways I ran a simulation and A is right on the money.
B says) Nope!
E says) 650 / 51

gAr · 2011-05-26 23:05:55

Hi bobbym,

bobbym · 2011-05-27 00:26:33

Hi gAr;

That is a nice idea. Let me know when you would like to see the answer.

gAr · 2011-05-27 00:35:33

Ok, but is my answer correct?

bobbym · 2011-05-27 00:36:37

It sure is!

gAr · 2011-05-27 00:52:26

Hmmm, I still don't get it! I'd like to see your solution.

bobbym · 2011-05-27 01:09:40

Mistake spotted. I have been writing black when I meant red. I changed that. Sorry for the error.

gAr · 2011-05-27 02:27:04

Hi bobbym,

Sometimes I feel I'm missing something here, sometimes I feel it's correct beyond doubt!
I concluded this:
It's equiprobable that there's an adjacent pair of red cards, with a probability 26*25/(52*51).
52 pairs are possible, hence E = 52 * p = 650/51.
Did you mean the same thing?

Similarly, we can conclude for 3 adjacent reds to be:

Isn't it?

bobbym · 2011-05-27 02:33:01

Hi gAr;
I wish I could be sure. I am confused about it. Based on the formula that is what is being done.

gAr · 2011-05-27 02:47:17

Okay!
I find combinatorics involving circular arrangement very confusing!
I can only backtrack from a simulation.

bobbym · 2011-05-27 02:53:27

Most forms of math have methods of checking your answer at the end.

Combinatorics and Probability often do not. This has wide ranging consequences and is the best reason why programming and computers are super important to math. They allow us to check!

Andrew Wiles wrote:

I never use a computer.

Answer: You never do any combinatorics or probability!

gAr · 2011-05-27 03:05:53

Yes, you're right.
And I can't believe Andrew Wiles said that! He's missing a great deal of mathematics.

bobbym · 2011-05-27 03:27:53

It is not a written quote, I actually heard him say it.

There is a controversy going on in math. Sometimes it is called Discrete math vs. Continuous math. Actually it is the debate between those who feel that math is an experimental science and those who do not. In the past math was done experimentally. Newton and Gauss are the prime examples. Today it is not. The main opponents of experimental math are Sir Michael Atiyah and Andrew Wiles...

The effects of many mathematicians disliking computers has filtered down into education. Most of the people who post on math forums have no idea that Mathematics works on numbers as well as letters. Take this post as an example:

Caushy Root Law is applicable on this question. And it can also be solved by applying the limits on it. The answer of the Question is 3.

You only have to try two numbers to see that the answer of 3 is wrong. But the concept of trying numbers, experimenting, is foreign to him. On another forum they like to pose a lot of inequalities. It never occurs to them to try a few numbers in there. Sometimes you can refute their conjectures by only trying 2 or 3 small integers.

gAr · 2011-05-27 03:56:08

If mathematics is to be the queen of sciences, how can anyone disapprove experimenting?!
What is science without experiments?!!

I remember that sequence sum, which I solved with a generating function.

Even those who refute it must have used proof by counterexamples at some time!

bobbym · 2011-05-27 04:11:01

I believe it is an experimental science. It is a minority viewpoint.

Trouble is the non - experimentalists control the educational system. They control the publication of articles. The allocating of grant money and teaching positions. The result is that most of todays students do not understand the relationship between math and numbers. That is why they think it is a dry, boring subject that has no relationship to the real world.

gAr · 2011-05-27 04:29:01

Yes. I believe that'll gradually change.

bobbym · 2011-05-27 04:42:01

That is where everyone splits again. There are those who believe it will get better and there are those who believe it will get worse.

I went to the best schools in my state. Supposedly getting the best math education anywhere, right? Nope, my math education was so poor that I had to drop my intended vocation. I thought all math questions had answers of the form 1, 2, 3, 1/2, 1/3 and √ 2

When they began to finally introduce us into math in my chemistry classes, I nearly fainted. Yes, differential equations are tough. But that is not what I and classmates, whom had the same education found tough. We could not get scientific notation!!!! Never saw any numbers that were not integers! My brother told me the first time in physics class he used a calculator and the answer was a decimal he thought the calculator made a mistake! No effort had been made in math classes to establish the fact that math was real. That it works on numbers. That numbers stand for real things. That answers in the real world are not 4.

The non-experimentalists had won. We live in their world right now.

gAr · 2011-05-27 05:37:03

Hmmm, yes, I get it.

Everybody likes to live their own way.

bobbym · 2011-05-27 05:38:21

Yes, I get carried away. My brother says I can put anybody to sleep.

gAr · 2011-05-27 05:52:20

Not me, yet!

bobbym · 2011-05-27 05:58:05

I was at a site which I lost but he does the same thing we are doing for this problem.

gAr · 2011-05-27 05:59:50

The same problem too?

bobbym · 2011-05-27 06:09:43

His was for adjacent pairs. He told me what I forgot.

E(X1 + X2) = E(X1)+E(X2) even when the random variables X1 and X2 are not independent! That is what I forgot. That is why you can multiply by 52.

http://tech.groups.yahoo.com/group/math … sage/12744

gAr · 2011-05-27 06:15:27

Ok, I'll check tomorrow. Feeling drowsy now. See you tomorrow.

Last edited by gAr (2011-05-27 06:16:01)

Math Is Fun Forum

#601 2011-05-04 00:24:40

Re: Is this cool with you?

#602 2011-05-26 08:38:24

Re: Is this cool with you?

#603 2011-05-26 23:05:55

Re: Is this cool with you?

#604 2011-05-27 00:26:33

Re: Is this cool with you?

#605 2011-05-27 00:35:33

Re: Is this cool with you?

#606 2011-05-27 00:36:37

Re: Is this cool with you?

#607 2011-05-27 00:52:26

Re: Is this cool with you?

#608 2011-05-27 01:09:40

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#609 2011-05-27 02:27:04

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#610 2011-05-27 02:33:01

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