Five undercover agents from an elite special force unit are caught by a criminal organization. The gangster leader decides to execute them by playing a deadly game. Anyone who can survive from this game will be released without a single wound. These are the details of the game:
The agents are given an opportunity to gather for a day before the game is started. After long discussion, one of the agents, the smartest one, has the best strategy to survive from the game. The strategy will yield the greatest number of agents that can be saved. Assume that, no matter what happens, all the agents will follow the strategy and since they are from the elite special force unit, it is reasonable to assume that they are all physically and mentally healthy so no one will ruin the plan. If the expected rate of survival using the best strategy can be expressed as \(\dfrac{p}{q}\), then what is \(p+q\)?
Next step : The Game of Death (Part II)