A fair coin is tossed three times. What is the probability that it lands “heads” at least once? In a coin-tossing game, a player tosses five fair coins. If he is content with the result, he stops. If not, he picks up one or more of the coins and tosses them a second time. If he is still dissatisfied, he may for one last time pick up and throw again one or more of the coins. Show that if the player’s aim is to finish with five heads showing, and if he uses the best strategy, then the probability that he will succeed is ( 7/8 )5. A second player plays the same game but aims to finish with either all heads or all tails showing. What is the probability of his succeeding?