Lottery game: What should the probability for the $1000 prize be set at?

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oregon789

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The state of Oregon wishes to design a new lottery game with the following rules:
- each ticket costs $5

- there will be three prizes: $10, $100, and $1000

- the probability of the $10 prize will be 20%
-the probability of the $100 prize will be 1%
-ten thousand tickets will be sold each month


What should the probability for the $1000 prize be set at, if the state would like, on average, to earn $10,000 each month?




Not sure how to set this up since the probability for the $1000 prize is unknown.
 
oregon789 said:
The state of Oregon wishes to design a new lottery game with the following rules:
- each ticket costs $5

- there will be three prizes: $10, $100, and $1000

- the probability of the $10 prize will be 20%
-the probability of the $100 prize will be 1%
-ten thousand tickets will be sold each month


What should the probability for the $1000 prize be set at, if the state would like, on average, to earn $10,000 each month?




Not sure how to set this up since the probability for the $1000 prize is unknown.
Click to expand...

Let the probability of winning $1000 be p.

Earning an average of $10 000 per month is the same as earning an average of $1 per ticket.

Expected earnings = 5 x 1 - (10 x 0.2 + 100 x 0.01 + 1000 x p) = 1
 
Nice!

Harry_the_cat said:
Let the probability of winning $1000 be p.

Earning an average of $10 000 per month is the same as earning an average of $1 per ticket.

Expected earnings = 5 x 1 - (10 x 0.2 + 100 x 0.01 + 1000 x p) = 1
Click to expand...

@oregon789 - No matter what it's suppose to be, we are not going to win it :) - Stay away from the lottery bud.
 
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