In a game of chance a player throws a pair of dice and scores points equal to the difference between the numbers on the two dice. Winner is the person who scores exactly `5` points more than his opponent. If two players are playing this game only one time, then the probability that neither of them wins toA. `(1)/(54)`B. `(1)/(108)`C. `(53)/(54)`D. `(107)/(108)`

In a game of chance a player throws a pair of dice and scores points e

1.	In a game of chance a player throws a pair of dice and scores points equal to the difference between the numbers on the two dice. Winner is the person who scores exactly `5` points more than his opponent. If two players are playing this game only one time, then the probability that neither of them wins toA. `(1)/(54)`B. `(1)/(108)`C. `(53)/(54)`D. `(107)/(108)`
Answer» Correct Answer - C `(c )` Player `A` can win if `A` throws `(1,6)` or `(6,1)` and `B` throws `((1,1),(2,2),(3,3),(4,4),(5,5) or (6,6))`. Thus the number of ways is `12`. Similarly the number of ways in which `B` can win is `12`. Total number of ways in which either `A` wins or `B` win `=24` Thus the number of ways in which none of the two wins `=6^(4)-24`. `:.` The required probability `=(6^(4)-24)/(6^(4))=(53)/(54)`

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