Suppose there exists a mini-lotto game, where each ticket costs $2, and a winning ticket allows...

 

 

 

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Suppose there exists a mini-lotto game, where each ticket costs $2, and a winning ticket allows you to cash it in for $1,000 (which goes directly in the winning player's pocket). Suppose that each ticket has a 1/600 chance of winning, and that all tickets are independent of each other, which in particular means that multiple wins are possible without changing the individual probability of obtaining a winning ticket. Right now, Person A and Person B both have $9,000 in their pockets. Person A decides that she is going to buy 1,800 tickets and person B decides that he is going to buy 3,600 tickets. Ariswer the following: a) b) c) d) What is the probability that, after all tickets are bought, all tickets are checked for winners, and all winners have been cashed in, Person A has exactly $10,400 in her pocket? (Your answer should be an exact answer with an Excel formula coded into your cell.) (Hint: First determine how many wins are required for Person A to have $10,400, and then use that information to answer the question.) Let X be the random variable that counts the number of winning tickets of person A. Find the expected value of X as well as the standard deviation of X. Expected value of X Standard deviation of X Let Y be the random variable that counts the number of winning tickets of person B. Find the expected value of Y as well as the standard deviation of Y. Expected value of Y Standard deviation of Y Let A represent the final amount that Person A has in her pocket after all tickets are bought, checked, and cashed, and let B represent the final amount that Person B has in his pocket after all tickets are bought, checked, and cashed. Which is larger, E(A) or E(B)? Highlight your answer and be sure to provide a brief justification of your answer. (Note that you are not required to actually calculate the expected values, only determine which will be larger, and why.) Justification: E(A) E(B) The decision tree below depicts a generic situation with the goal of minimizing (!) expected value. Note that the tree has been setup but not rolled back. Please rollback the decision tree by filling in the four bold, green cells. To receive credit, you must either code your answer cells with a formula/cell-references or you may choose to re-create the decision tree to the right of this tree so that the cells auto-populate in the tree you create. TreePlan Student License Alternative 1 -10 Alternative 2 -20 0.5 Outcome 3 30 0.5 Outcome 4 40 0.1 Outcome 8 30 0.9 Outcome 9 40 20 10 20 4 0.3 Outcome 5 10 0.6 Outcome 6 20 0.1 Outcome 7 5 40 50 35 20 40 50 35 10 20 Suppose there exists a mini-lotto game, where each ticket costs $2, and a winning ticket allows you to cash it in for $1,000 (which goes directly in the winning player's pocket). Suppose that each ticket has a 1/600 chance of winning, and that all tickets are independent of each other, which in particular means that multiple wins are possible without changing the individual probability of obtaining a winning ticket. Right now, Person A and Person B both have $9,000 in their pockets. Person A decides that she is going to buy 1,800 tickets and person B decides that he is going to buy 3,600 tickets. Ariswer the following: a) b) c) d) What is the probability that, after all tickets are bought, all tickets are checked for winners, and all winners have been cashed in, Person A has exactly $10,400 in her pocket? (Your answer should be an exact answer with an Excel formula coded into your cell.) (Hint: First determine how many wins are required for Person A to have $10,400, and then use that information to answer the question.) Let X be the random variable that counts the number of winning tickets of person A. Find the expected value of X as well as the standard deviation of X. Expected value of X Standard deviation of X Let Y be the random variable that counts the number of winning tickets of person B. Find the expected value of Y as well as the standard deviation of Y. Expected value of Y Standard deviation of Y Let A represent the final amount that Person A has in her pocket after all tickets are bought, checked, and cashed, and let B represent the final amount that Person B has in his pocket after all tickets are bought, checked, and cashed. Which is larger, E(A) or E(B)? Highlight your answer and be sure to provide a brief justification of your answer. (Note that you are not required to actually calculate the expected values, only determine which will be larger, and why.) Justification: E(A) E(B) The decision tree below depicts a generic situation with the goal of minimizing (!) expected value. Note that the tree has been setup but not rolled back. Please rollback the decision tree by filling in the four bold, green cells. To receive credit, you must either code your answer cells with a formula/cell-references or you may choose to re-create the decision tree to the right of this tree so that the cells auto-populate in the tree you create. TreePlan Student License Alternative 1 -10 Alternative 2 -20 0.5 Outcome 3 30 0.5 Outcome 4 40 0.1 Outcome 8 30 0.9 Outcome 9 40 20 10 20 4 0.3 Outcome 5 10 0.6 Outcome 6 20 0.1 Outcome 7 5 40 50 35 20 40 50 35 10 20