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
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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) (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
 = \sum_{i=0}^{\infty} \frac{5^{2k}}{6^{2k+1}})
^k)
(\frac{1}{1 - \frac{25}{36}}) = \frac{6}{11})
Therefore, the probability that A wins is 6/11, and the probability that B wins is 1 - (6/11), or 5/11.
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