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October 30th, 2013, 01:23 PM  #1 
Senior Member Joined: Oct 2009 Posts: 895 Thanks: 1  Two players A and B play a game of dice .
Two players A and B play a game of dice . They roll a pair of dice alternately . The player who rolls 7 first wins . If A starts then find the probability of B winning the game ? please help me how I can solve this question 
October 30th, 2013, 01:47 PM  #2 
Senior Member Joined: Feb 2012 Posts: 628 Thanks: 1  Re: Two players A and B play a game of dice .
Well, the probability of rolling a 7 is 1/6, so the probability of not rolling a 7 is 5/6. If A goes first, he must not roll a 7 in order for B to win. So this has a 5/6 chance of occurrence. Then, if B rolls a 7, B wins. This has a chance of 1/6. So the probability of B winning after one round is . But this is the probability of B winning in any round, given that neither player has won yet. The probability that neither player wins in a given round is . Hence, the probability that B wins in the nth round is . The probability that B wins is then . 
October 30th, 2013, 01:59 PM  #3 
Senior Member Joined: Oct 2009 Posts: 895 Thanks: 1  Re: Two players A and B play a game of dice .
How you got A ) that the probability of rolling a 7 is 1/6 ? B ) the probability that neither player wins in a given round is 25/36 thanks 
October 31st, 2013, 11:37 AM  #4 
Senior Member Joined: Feb 2012 Posts: 628 Thanks: 1  Re: Two players A and B play a game of dice .
A) There are 36 possible rolls for two dice, since there are 6 possibilities for the first die and 6 possibilities for the second die. Of these, there are 6 combinations that yield a sum of 7: (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1). This gives a chance of rolling a 7. B) Since there is a 1/6 chance of either player rolling a 7, there is a 5/6 chance that A will not roll a 7, and a 5/6 chance that B will not roll a 7. Since these two events are independent, the probability of both of them occurring in one round is the product of both chances, which is . 
October 31st, 2013, 12:44 PM  #5  
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 10,683 Thanks: 700  Re: Two players A and B play a game of dice . Quote:
1st roll : 3 2nd roll: only a 4 will make 7, so 1/6 Works similarly for any 1st roll result: 16, 25, 34, 43, 52, 61  
October 31st, 2013, 03:49 PM  #6 
Senior Member Joined: Oct 2009 Posts: 895 Thanks: 1  Re: Two players A and B play a game of dice .
thanks all now is clear


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