Play the following games in the Games Fair:

• Three Prize Roller
• Word Scramble
• Marble Draw
• Ten Spinner - Note: It is 10 sections where each has a 30% chance of being green.

a) For each Games Fair game, answer the following questions:

1. Create the probability distribution in a table for all the outcomes where X is the random variable representing the number of points awarded.
2. Communicate how you arrived at the probability of each outcome.
3. What is the expected value, E(X), for the game? You may include this in your table from the distribution. If the game costs 10 points to play, how much would the player expect to win or lose?
4. Create the bar graph for the Probability Distribution.

b) For each of the 4 Games Fair games above, suggest an improvement to the rules and justify why you have suggested that and what the change in expected value would be. Your improvement could be changing the point outcomes to make the game more appealing or a change in the game itself keeping the same theme. For example, for the Ten Spinner game in the Games Fair, you could change it to 8 or 12 sections.