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Mathematical Expectation Making the game fair

Mathematical Expectation Making the game fair. Make the Bet = X (we need to figure it out) Create the Table Under the column for outcome (O) subtract x from the gain Set up the Equation M.E. = p 1 o 1 + p 2 o 2 +p 3 o 3 etc Make the M.E. = 0 .

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Mathematical Expectation Making the game fair

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  1. Mathematical ExpectationMaking the game fair

  2. Make the Bet = X (we need to figure it out)Create the TableUnder the column for outcome (O)subtract x from the gainSet up the EquationM.E. = p1o1 + p2o2 +p3o3 etcMake the M.E. = 0

  3. Determine the amount of the bet to make the following game fairRoll a dieIf you roll a 1 you win $10 If you roll a 6 you win $5Any thing else you lose your betn.b. the bet is included in the wins

  4. Let x = the bet M.E. = 1.7 – 0.17x + 0.85 – 0.17x – 0.67x 0 = 2.55 – x X = 2.55 The bet would have to be $2.55 for this game to be fair

  5. The Table M. E. = 1.7 - .00017x + .34 – 0.00017x + .17 – 0.00017x -.9995x M. E. = 0 0 = 2.21 – x X = 2.21 The ticket price would have to be $2.21 but it wouldn’t be much of a fundraiser would it?

  6. Changing the M.E. Joe bets $1 on the roll of a die If he rolls a 4: he wins $5 plus his bet 2: he wins $1 plus his bet 5: he gets his bet back Is it fair? M.E. = 0.85 + 0.17 + 0 – 0.5 = 0.52 Change the bet to make this game fair Change an outcome to make this game fair

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