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October 30th, 2013, 01:23 PM   #1
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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
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October 30th, 2013, 01:47 PM   #2
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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 .
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October 30th, 2013, 01:59 PM   #3
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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
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October 31st, 2013, 11:37 AM   #4
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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 .
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October 31st, 2013, 12:44 PM   #5
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Re: Two players A and B play a game of dice .

Quote:
Originally Posted by r-soy
How you got
A ) that the probability of rolling a 7 is 1/6 ?
Example:
1st roll : 3
2nd roll: only a 4 will make 7, so 1/6

Works similarly for any 1st roll result: 1-6, 2-5, 3-4, 4-3, 5-2, 6-1
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October 31st, 2013, 03:49 PM   #6
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Re: Two players A and B play a game of dice .

thanks all now is clear
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