AP Statistics Games of Chance and Expected Value Expected value is a way of measuring what the long-term outcome of repeated trials of an experiment...

AP StatisticsGames of Chance and Expected ValueExpected value is a way of measuring what the long-term outcome of repeated trials of anexperiment will be. This method is often used to determine the fairness of games of chance.Nearly every game of chance has an expected value less than the cost of playing the game. If thiswere not true, these games would not be fund-raisers for governments, churches, and othercharity groups. Casinos are also run in such a way to guarantee themselves profit. With thisconcept of expected value in mind, complete the following tasks and write up the results in areport.Task 1. Consider rolling one (six-sided) fair die and tossing one (two-sided) fair coin. If thecoin turns up heads, then the number of spots showing on the die is the score of that trial. If thecoin turns up tails, then twice the number of spots showing on the die is the value for that trial. Inother words, if the coin-toss results in a head and the die lands showing a 4 face up, then thescore is 4 points for that trial. If the coin were to land tails up and the die landed a 4 face up, thenthe score of that trial will be 8 points. Determine the possible outcomes in the sample space andconstruct a probability distribution table. Once that is completed you are to find the expectedvalue of the following experiment. If I were to invite you to play the above game where I wouldpay you your score in dollars (1 point = 1 dollar), what should I charge you to play? Using thatticket price, how many games would have to be played in order for me to have an expected profitof $100.00?Task 2. Let’s consider the “same” experiment and scoring scheme in Task 1 except that nowthe die is “weighted” so that the probability of getting the various rolls of the die is as follows:61/12Find the expected value (don’t forget the coin toss). In order to make a little profit in the “longrun”, what should your minimum charge be for the privilege of playing this game?Task 3. The NC Education Lottery contains many games of chance. While it is certainly not theintent of this project to invite you to play the games of the lottery it does, nevertheless, providesome real world examples of probability outcomes and expected values. Go to the websitehttp://www.nc-educationlottery.org/pick3.aspx and look at the rules for the “Carolina Pick 3”game (school computers have blocked this website so you will need to do this at home).Compute the expected value of one ticket purchased and compare that to the actual purchaseprice of the ticket.

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