Math Is Fun Forum

dhs9

Member

Registered: 2006-08-28

Posts: 1

Calculating odds of specific order of group of people

Math was never my strong suit so I defer to the experts to assist me with this problem.  Assume a group of 20 people are sitting in a circle with the moderator sitting at the 12:00 position ( the moderator is not counted in the group of 20 as his position always stays the same).  What are the odds of 2 specific individuals of this group being situated at the same time next to the moderator. It does not matter if the individuals are to the right or left of the moderator only that both are next to him at the same time.

Thanks so much for your help.  I hope I provided enoug info to solve this problem.

Dave

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Calculating odds of specific order of group of people

Don't worry, you've explained it very well.

Let's look at the first person (who I've decided is called Aaron) who wants to sit next to the moderator. (And good on him by the way, moderators are awesome )

There are 19 possible places that Aaron could sit and 2 of them are good, the one to the left or the moderator and the one to the right. So the chance of Aaron getting a seat he likes is 2/19.

Aaron has been placed already, so now the 2nd person, Beatrice, has 18 possible seats and only one of them is next to the moderator, because Aaron already took the other one. So Beatrice has a 1/18 chance of getting to sit next to the moderator.

To work out the chance that both of these things happen, we multiply them together. 1/18 * 2/19 = 2/342 = 1/171.

So the chance that both Aaron and Beatrice get to sit next to the moderator is 1/171.

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Why did the vector cross the road?
It wanted to be normal.