一道英文概率题Consider the following version of the game of craps：The player rolls two dice.If the sum on the first roll is 7 or 11,the player wins the game immediately.If the sum on the first roll is 2,3 or12,the player loses the game immed
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一道英文概率题Consider the following version of the game of craps：The player rolls two dice.If the sum on the first roll is 7 or 11,the player wins the game immediately.If the sum on the first roll is 2,3 or12,the player loses the game immed
一道英文概率题
Consider the following version of the game of craps：The player rolls two dice.If the sum on the first roll is 7 or 11,the player wins the game immediately.If the sum on the first roll is 2,3 or12,the player loses the game immediately.However if the sum on the first roll is 4 5 6 8 9 or 10,then the two dice are rolled again and again until the sum is either 7 or 11 or the original value.If the original value is obtained a second time before either 7 or 11 is obtained,then the player wins.If either7 or 11 is obtained before the original value is obtained a second time,then the player loses.Determine the probability that the player will win this game.
一道英文概率题Consider the following version of the game of craps：The player rolls two dice.If the sum on the first roll is 7 or 11,the player wins the game immediately.If the sum on the first roll is 2,3 or12,the player loses the game immed
2 3 4 5 6 7 8 9 10 11 12
1/36 2/36 3/36 4/36 5/36 6/36 5/36 4/36 3/36 2/36 1/36
7 or 11 8/36=2/9 win on first roll
2 3 or 12 4/36=1/9 lose on 1st roll
else 24/36 =2/3 continue from first roll
p of obtaining original value from second roll=1/36
p of contuinuning the game from second roll and after=(2/3-1/36)=23/36
(2/9)+(2/3)(1/36)+(2/3)*(23/36)*(1/36)+(2/3)*(23/36)^2(1/36)+.
=2/9+(2/3)(1/36)(1+23/36+(23/36)^2+(23/36)^3.)
=2/9+(2/3)(1/36)/(1-23/36)
=2/9+(2/3)(1/36)(36/13)
=2/9+2/39
=26/117+6/117
=32/117