1. A game has three boxes. Box 1 has one drawer, Box 2 has two drawers, and Box 3 has three drawers. You will pick a box at random and then pick a drawer from that box at random.
a. A prize is hidden in the top drawer of Box 3. What is the probability that you select this drawer?
b. A prize is hidden in the only drawer of Box 1. What is the probability that you will select this drawer?
2. Consider a box game with 2 boxes. Box 1 has one drawer, and Box 2 has 5 drawers. A player will select a box at random and then pick a drawer from that box at random. You have two prizes to place in the drawers. Where should you place them to create the greatest probability that someone who plays the game will win a prize? Explain your reasoning.
I would place the prize in Box 2 because it has the most outcomes which gives the player more chances to select the drawer that containers the prize.