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In a hockey match, both teams A and B scored same number of goals up to the end of the game, so to decide the winner, the referee asked both the captains to throw a die alternately and decided that the team, whose captain gets a six first, will be declared the winner. If the captain of team A was asked to start, find their respective probabilities of winning the match and state whether the decision of the referee was fair or not.

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Let S denote the success (getting a '6')  and F denotes the failure (not getting a '6')

Thus P(S) = 1/6, P(F) = 5/6

P(A wins in the first throw) = p(S) = 1/6,

A gets the third throw, when the first throw by A and second throw by B result into failures. Therefore, P(A wins in the 3rd throw)

Decision : Referee's decision was fair because team spirit enhances co-operation and unity

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