"Inside  every small problem is a large problem struggling to get out."

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Respond to the question: Probability?

 04/30/2002 07:50 PM by OMuenchoww; Probability
Hello,

My name is Dr. Otto Muenchow. I am a pediatrician here in the Los Angeles area. I have always been facinated with the particular subject of Game Theory. I have not really had the time to pursue reading material on the subject matter until last week. I picked up a Game Theory book by a Mr. Ralph Keeny. In it he explains the very basic aspects of different games etc. There are a few problems though throughout the book where Mr. Keeny does not provide an answer. And few he would provide answers but no solution. These problems are interspersed in the middle or at the end of chapters almost as an afterthought (in quotations).

I am writing you b/c one of my collegues who also is a fan of this under-studied art had given me a list of websites I should visit if I had any particular questions or wanted to know more. I was hoping you could shed some light on the a few of these problems.

“Why is the number of different ways that r people can be seated in r ordered chairs is r! Try and think of an example.”

“Explain why the number of different ways that r people can be seated in n>r ordered chairs is n! / (n-r)! Again, think of an example.”

“Why is the number of ways to place r identical objects in n>r ordered chairs is

n! / [r!(n-r)!]. Where else can you also use this way of counting to help compute a probability?”

“In repeated independent trials with only two outcomes, say success and failure, where the probability of success is always p in each trial, the probability of having r success in n trials is given by the binomial distribution as

P(r successes | n trials, p success prob) = n! / [r! (n-r)!] * p r * (1-p) (n-r)

Explain why this makes sense and see if you can think of an illustration.”

On the third one, isn't that statement a binomial coefficient denoted as nCr? Is it read n chooses r? (just wondering). Thank you in advance for your time and patience. I look forward to hearing form you

Regards,

Otto Muenchow

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