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: nCx * 80-nC20-x We also saw the total number of possible outcomes in Club Keno are 80C20. Four Numbers - Expected Value According to the Michigan 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.
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:
nCx * 80-nC20-x
We also saw the total number of possible outcomes in Club Keno are 80C20.
Four Numbers -
According to the Michigan 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 probabilities as decimals, rounded to four decimal places.
| Outcome |
Probability (Use Scientific Notation) |
Net Value (Don't forget to account for the $1 bet) |
Product (Round to 3 decimals) |
| 4 correct |
|
$
|
$
|
| 3 correct |
|
$
|
$
|
| 2 correct |
|
$
|
$
|
| 0 or 1 correct |
|
$
|
$
|
What is the expected value if you choose four numbers? $
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