Play the following games in the Games Fair Three Prize Roller each roll of the die costs 10 points You win 10 points if you roll a two, 20 points if you roll a four, 28 points If you roll a 6 Word Scramble it costs 10 points to scramble the letters in the word LUCK You win 0 points if only the first letter is in the right spot 5 points if only the second letter is in the right spot 10 points if only the third letter Is in the right spot 15 points if only the fourth letter is in the right spot 20 points if 2 letters including the first are in the right spot 25 points if two letters not including the first are in the right spot 40 points if all letters are in the correct spot For each Games Fair game, answer the following questions Create the probability distribution in a table for all the outcomes where X is the random variable representing the number of points awarded Communicate how you arrived at the probability of each outcome 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 Create the bar graph for the Probability Distribution For each of the Games Fair games, suggest an improvement to the rules andjustifywhy 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 Add the improvement to your document

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Play the following games in the Games Fair: Three Prize Roller=each roll of the die costs 10 points. You win 10 points if you roll

Play the following games in the Games Fair:

Three Prize Roller=each roll of the die costs 10 points. You win 10 points if you roll a two, 20 points if you roll a four, 28 points If you roll a 6.
Word Scramble= it costs 10 points to scramble the letters in the word LUCK. You win 0 points if only the first letter is in the right spot. 5 points if only the second letter is in the right spot. 10 points if only the third letter Is in the right spot. 15 points if only the fourth letter is in the right spot. 20 points if 2 letters including the first are in the right spot. 25 points if two letters not including the first are in the right spot. 40 points if all letters are in the correct spot.

For each Games Fair game, answer the following questions:

Create the probability distribution in a table for all the outcomes where X is the random variable representing the number of points awarded.
Communicate how you arrived at the probability of each outcome.
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?
Create the bar graph for the Probability Distribution.

For each of the Games Fair games, suggest an improvement to the rules andjustifywhy 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. Add the improvement to your document.