Round and round (IME-JEE 2015)
Three players sit around a table and play, one at a time, a non-crooked 6 faced-dice. The first player throws the dice, followed by the other at his left, continuing this way until the game ends.
The winner is the player who throws a dice and its result is 6 , then the game ends. If one player gets a 1 , the next player will lose his turn.
The game will go on until someone wins.
What's the probability for the first player to win?
This problem was on the discursive phase of IME-JEE from Brazil.
The answer is 0.405.
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