SOLUTION: Pls help me solve this question A and B play the following game.They throw alternatively a pair of dice.Whosoever gets sum of two numbers on the top as 7 wins the game and the g

Algebra ->  Probability-and-statistics -> SOLUTION: Pls help me solve this question A and B play the following game.They throw alternatively a pair of dice.Whosoever gets sum of two numbers on the top as 7 wins the game and the g      Log On


   

Question 518919: Pls help me solve this question
A and B play the following game.They throw alternatively a pair of dice.Whosoever gets sum of two numbers on the top as 7 wins the game and the game stops.Suppose A starts the game,find the probability that
a)A wins the game
b)B wins the game
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
The probability of getting a 7 on two dice is 1/6.

The probability that A wins right away is 1/6. Hence, the probability that B wins right away is (5/6)(1/6) = 5/36.

The probability that A wins on his second throw is (5/6)(5/6)(1/6) = 25/216. Hence, the probability that B wins on his second throw is (5/6)(5/6)(5/6)(1/6) = 125/1296.

We repeat this pattern to obtain







Therefore, the probability that A wins is 6/11, and the probability that B wins is 1 - (6/11), or 5/11.