A bowl contains three candies: two red and one green. Work with a partner and decide who is player A and who is player B. Then take turns choosing a candy from the bowl without looking. Player A takes one and holds on to it, then player B takes one. If the colors match, player A gets a point; if they differ, player B gets a point. Is this a fair game? First try the game experimentally. Then show your analysis of the probabilities.

Now put four candies in the bowl, three of one color and one of another. Will this game be fair? Again, check experimentally then give your analysis using probabilities.

Are there other ways to put different numbers of two colors of candy in the bowl that would lead to a fair game while keeping the rest of the rules the same as in the previous two problems? Try a number of different possibilities (up to at least a total of 20 candies). Analyze each one using probability, make some hypotheses, and report any patterns you see in the results, conclusions, or generalizations that you can justify mathematically.