In the carnival game Chuck-a-Luck, you choose a number between 1 and 6. Then three fair dice are rolled. You win the game if the number you chose comes up on any of the three dice. Much to the pleasure of the carnival organizers, people sometimes wrongly reason that they have a 1 in 6 chance of their number appear on each die and so a 3 X 1/6 =1/2 probability of winning this game. This is incorrect. What is the actual probability that you will win this game?