Kicker Another option in Club Keno is to play the "Kicker." This is an option that doubles your bet, but you can get a random multiplier to your winnings. About 2/3 of the time there is no multiplier, though. Let's consider what the expected value is when playing the kicker while only betting on only one number. Outcome Kicker Probability Net Value 1 Correct x1 0. 15625 SO 1 Correct X2 0.046875 $2 1 Correct x3 0.0234375 1 Correct X4 0.01171875 1 Correct x5 0.00585938 $8 1 Correct x10 0.00585938 $18 0 Correct Any 0.75 -$2 What is the expected value when using the Kicker option and choosing one number? $ (Round to the nearest cent.) If you had not played the kicker, the table would be: Outcome Probability Net Value 1 Correct 0.25 $1 0 Correct 0.75 -$1 If you had not played the kicker, what would the expected value be? $ (Round to the nearest cent.) Submit and EndMichigan Lottery the best odds of winning are when you pick four numbers. If all four numbers come up then you win $72 for each dollar you bet. If three numbers come up then you win $5 for each dollar you bet. If two numbers come up then you win $1 for every dollar you bet (net winnings are zero). Otherwise, you lose the money you bet. Fill out the following table, assuming a $1 bet. Enter your probabilities as decimals, entering all the digits you see on your calculator. Net Value Product Outcome Probability (Don't forget to account for the $1 (Round to 3 bet) decimals) 4 correct $ 3 correct 2 correct $ 0 or 1 correct What is the expected value if you choose four numbers? $ Kicker Another option in Club Keno is to play the "Kicker." This is an option that doubles your bet, but you can get a random multiplier to your winnings. About 2/3 of the time there is no multiplier, though. Let's Nor10 pts 9 1 Here are the basic rules of Club Keno: . You choose how many numbers you will pick. You can pick anywhere from 1 to 10 different numbers. . Pick your numbers between 1 and 80. . A drawing is held in which 20 numbers are picked. . Depending on how many of your numbers come up in the drawing, you win various amounts of money. In a previous assignment we saw the number of ways to choose exactly x correct from a total of n picks, you would do: n x * 80-n 20-X We also saw the total number of possible outcomes in Club Keno are 80C20. Four Numbers - Expected Value According to the Michigan Lottery D the best odds of winning are when you pick four numbers. If all four numbers come up then you win $72 for each dollar you bet. If three numbers come up then you win $5 for each dollar you bet. If two numbers come up then you win $1 for every dollar you bet (net winnings are zero). Otherwise, you lose the money you bet. Fill out the following table, assuming a $1 bet. Enter your probabilities as decimals, entering all the digits you see on your calculator. Net Value Product Outcome Probability (Don't forget to account for the $1 (Round to 3 bet) decimals) S 4 correct $ 3 correct L JUN 2