(Adapted from the battle game "Bowser's Bigger Blast" from Nintendo's "Mario Party 4") In this game, 4 players compete in a deadly game of chance against each other.
On a stage, there are 5 detonators.
One is connected to a bomb while the other four are disconnected and will have no effect.
Player 1 must go first and push one of the five detonators. If he is unlucky enough to choose the live detonator, he will set off the bomb and lose the game (and his life). If he chooses one of the four "duds," he is safe and will remove that detonator from the game. At that point, player 2 must choose one of the four remaining detonators, and so on. If all four players are lucky enough to survive their choices, then the stage is reset (with the five detonators and one randomly selected to be live) and the procedure is repeated, until a player eventually loses. Is this a fair game?
Or, is one player more likely to lose than the others? That is, find the probability of each player losing the game.