Combinatorics: Spreading Rumors and Probability

[Shoney45]

Homework Statement

A rumor is spread randomly among a group of 10 people by successively having one person call someone, who calls someone and so on. A person can pass the rumor on to anyone except the individual who just called.

What is the probability that if A starts the rumor, A receives the third call?

Homework Equations

none

The Attempt at a Solution

I'm having difficulty getting started with this one. If person A starts the rumor, then the way the question is worded, it would appear that A could choose any ten people that happen to live on planet Earth who happens to own a telephone. So that's got me real confused and I don't know how to start.

 

[tiny-tim]

Hi Shoney45!

A rumor is spread randomly among a group of 10 people by successively having one person call someone, who calls someone and so on.
…
If person A starts the rumor, then the way the question is worded, it would appear that A could choose any ten people that happen to live on planet Earth who happens to own a telephone. So that's got me real confused and I don't know how to start.

No, it means a fixed group of 10 people.

 

[Shoney45]

Hi Shoney45!


No, it means a fixed group of 10 people.

Cheers Tiny Tim! And thanks for your smiles!

So are you understanding the problem to say that the set of people which can be called to spread the rumor to consists of only ten people? So in other words, if A starts the rumor, and then calls those ten people, are you understanding the question to mean that that set of people who can be called with the rumor is the same set of ten people who were just called and given the rumor, and so on for any successive calls?

It doesn't much sound like rumor spreading to me, but if that is the problem then I will go with it.

 

[tiny-tim]

Hi Shoney45!

It doesn't much sound like rumor spreading to me, but if that is the problem then I will go with it.

The people who set these questions only know approximately nine other people.

 

[Shoney45]

Hi Shoney45!


The people who set these questions only know approximately nine other people.

Sweet! Well, I guess I'll wrestle with the problem under this set of shiny new asumptions.