Homework Help: Mathematical Probability Question

1. Feb 12, 2010

Legendre

I spent quite a lot of time trying to figure out this question that I read in a book. Through trial and error, I got a rough idea of what the solution should be like but can't figure out how I would derive it mathematically. Can anyone give me some directions? :)

QUESTION:

n people stand in a circle, where n > 2. we pick two person, A and B, at random. what is the probability that there are exactly r people standing in between A and B, in the clockwise direction?

2. Feb 12, 2010

tiny-tim

Hi Legendre!

Can you think of a way of simplifying the question?

3. Feb 12, 2010

elibj123

Given a choice of A, how many B's will satisfy the condition?

4. Feb 12, 2010

tiny-tim

Yup!

(or, rather, what proportion of B's will satisfy the condition?)

So you can simplify the problem by arbitrarily fixing A, which makes the answer … ?

5. Feb 12, 2010

Redbelly98

Staff Emeritus
Moderator's note: thread moved to Homework forums.

6. Feb 15, 2010

Legendre

Thanks for not outright giving the answer! I find that I learn much more if I were to come out with an answer using hints.

Now lets see...

Fix A. Counting in the clockwise direction, only 1 B satisfies "exactly r people are standing between A and B".

0 <= r <= (n-2). So there are (n-1) possible r.

So the probability is 1/(n-1).

7. Feb 15, 2010

tiny-tim

(just got up :zzz: …)
Woohoo!

8. Feb 15, 2010

haha thanks!