Answer Happy

You work at a casino where your boss wants you to help her develop a new game. In that game, a person rolls two fair six-sided dice. If a person rolls more than a sum of 7 , it is considered a win. They roll the two dice a total of 5 times. This means they could have anywhere from 0 wins to 5 wins. Prizes and the amount of the prize for various wins are listed below. Your boss wants you to figure out how much to charge for the game. If you charge too much money, a person won't want to play the game. If you charge too little money, you might not make up for the cost of the prizes being given away. Determine the probability of winning each type of prize and how much should be charged if the company wants to break even. (Break even means the company wins $0 on average in the long run.)
Here are the probabilities for rolling a certain number with a two dice roll: 1. Using the above table, determine the probability of winning (i.e., rolling a MORE THAN A SUM OF SEVEN) on any given roll? 2. Since each roll is independent, and the number of trials is fixed, and the probability of winning doesn't change from roll to roll, this means that the probabilities of winning prizes follows a binomial distribution. Use the binomial distribution to complete the probability distribution function (hint: you might want to use the Mod 4 Google Sheet as a model for this) 3. Combine the probabilities that you developed with the prize amounts to answer this question: what is the expected value of the game? (Hint: you might want to use the FIRST tab on the Mod 4 Google Sheet as a model for this). Please show your work by pasting/typing a table. 4. How much do you think you should charge people to play the game? Why do you say that?