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The Dice Game (Posted on 2003-11-10) Difficulty: 3 of 5
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?

See The Solution Submitted by Gamer    
Rating: 4.2500 (4 votes)

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Solution solution | Comment 1 of 6
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 5/6x and A's chance is 25/36x.... and this must total one.

So we set it up:
x + 5/6x + 25/36x = 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
  Posted by SilverKnight on 2003-11-10 14:53:22
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