Play the following games in the Games Fair: Three Prize Roller: Roll 1 dice. You are rewarded in the following ways. 10 points if you roll a two, 20 points if you roll a four, or 28 points if you roll a six. Marble Draw: 15 marbles are in the bag, 7 of them are red. Draw 4 marbles without replacement, Rewards are given for: 0 red: 30 points, 1 red: 10 points, 2 red: 0 points, 3 red: 20 points, 4 red: 50 points. Do the following for each of the games: 1. Introduce your random variable X, ensuring it does NOT include the cost to play each game. Then create the probability distribution in table form for the number of points. Do not convert probabilities to percentages. Round probabilities to two decimal places. Your values of X should be presented in increasing order, and identical values should be combined. 2. Create the probability distribution for X in the form of a bar graph. Values of X should be in increasing order from left to right. Make sure your graph is properly labelled. X values that are identical should be combined. 3. Give a mathematical solution to show how you calculated the probability of each of the above values for X. Include all necessary steps in your calculation and remember to express final probabilities rounded to two decimal places. 4. What is the expected value, E(X), for the game? Show your calculation. 5. If the game costs 10 points to play, how much would the player expect to win or lose per game?