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 picked comes up on any of 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 as well as so a 3 X 1/6 =1/2probability of winning this game. This is incorrect. Determine the actual probability that you will win this game?
Assume that four women and two men enter the restaurant and sit at random around a table that has four chairs on one side as well as another four on the other side. Determine the probability that the men are not all sitting on one side?