In the new dice game costing $1 to play, two dice are rolled. If the result is prime number, the player wins $2 (that is, the original $1 plus another dollar). Otherwise, player loses his or her $1 bet. Is this a fair game?
A player joins the game and strangely loses the first 5 games. Determine the probability that it would take more than 5 games in order to win her first game?