perplexus.info :: Probability : The Dice Game

The Dice Game (Posted on 2003-11-10)

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?

Submitted by Gamer

Rating: 4.2500 (4 votes)

Solution: (Hide)

When B rolls, there is a 1/6 chance that he will win with his first roll. There is a 5/6 x 1/6 chance that C will win with his roll. (There is a 5/6 chance that B won't win and a 1/6 chance that C will match.) Then there is a 5/6 x 5/6 x 1/6 chance that A will win with his first roll.

Then there is a 5/6 x 5/6 x 5/6 x 1/6 chance that B will win on his second roll, and a 5/6 x 5/6 x 5/6 x 5/6 x 1/6 chance for C's second roll and a 5/6 x 5/6 x 5/6 x 5/6 x 5/6 x 1/6 chance for A's second roll

So, the probability of A winning is 5/6 the probability that C will win, and the probablilty of C winning is 5/6 the chance of A winning. The lowest integers that satisfy this are 36 for B, 30 for C and 25 for A. 36+30+25=91.

So, there is a 36/91 chance that B will win, a 30/91 chance that C will win, and a 25/91 chance that A will win.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
late jump solution	wonshot	2003-11-12 15:56:41
solution - not so nice as that of SK	Saso	2003-11-11 09:45:20
re: solution	Dan	2003-11-10 18:51:53
re(2): solution	SilverKnight	2003-11-10 15:05:35
re: solution	Cory Taylor	2003-11-10 14:59:43
solution	SilverKnight	2003-11-10 14:53:22

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