A and B throw a pair of dice alternately. A wins the game, if he gets a total of 7 and B wins if he gets a total of 10. If A starts the game, then find the probability that A wins.
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The probability of A winning is 2/ 3 or 66.67 %
See the images for full solution.
In short , total number of combinations by a pair of dice is 36.
in 6 out of 36 combinations , 7 is the sum.
in 3 out of the 36 combinations , 10 is the sum .
Therefore , the probability of A winning is ratio of
6/36 : 3/36
= 6 : 3
Which when converted in Percentage form will be ,
6 / (6+ 3) * 100
6/9 * 100
= 66.67 %
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