Three people, A,B,C play a game. A rolls the die.

Then, in order of "B,C,A,B,C,A..." they each roll the die. They keep going until someone wins. To win, you have to get the same number as the previous number rolled on the die. ( A can't win with his first roll because there was no roll before to compare it too.)
What is the probability that each person will win?

As Lee pointed out in his

"completeness" comment for a previous problem, the total probability must equal one.

And since person B is essentially the first player, B has the first and best chance of winning (of 1/6).

So... the others following are 5/6 as likely of winning as the previous player.

So, call B's chance

*x*. Then C's chance is 5/6

*x* and A's chance is 25/36

*x*.... and this must total one.

So we set it up:

*x* + 5/6

*x* + 25/36

*x* = 1

and x = 36/91

therefore,

B's chance is

**36/91**
C's chance is

**30/91**, and

A's chance is

**25/91**
*Edited on ***November 10, 2003, 2:54 pm**