Q25 of 26 Page 1

A, B and C throw a pair of dice in that order alternately till one of them gets a total of 9 and wins the game. Find their respective probabilities of winning, if A starts first.

Let E be the event of ‘getting a total of 9’ when two dice are thrown.

So, sum of 9 can be obtained, E = {(3,6); (4,5); (5,4); (6,3)}


So, the total possibilities of getting a total of 9 when two dice are thrown are 4


and Total Sample Space = 36






Now, it is given that there are 3 players A, B and C and they are throwing a pair of dice alternately.


This means A wins if he gets 9 in 1st or 4th or 7th throw and so on.


His probability of ‘getting 9’ in 1st throw


A will get the 4th throw if he fails to get 9 in the 1st throw, B fails in 2nd and C fails in 3rd throw





Similarly,





and so on.


Hence, the Probability of winning A







Now, we have to check the probability of winning of B


B wins if he gets 9 in 2nd or 5th or 8th throw and so on.


So, the Probability of winning of B








Hence, the Probability of winning of C


= [1 – {P(A winning) + P(B winning)}]






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