The state of Oregon wishes to design a new lottery game with the following rules

ID: 3174736 • Letter: T

Question

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?

Can someone please list the steps to solve this and how they got their answer with clear easy-to-read writing?

Let the probability of winning the $1000 prize be X then,

Expected Winning amount would be :( for each ticket )

= 10*(0.2) + 100(0.01) + 1000(X) becaise there is 20% chance of winning $10 and 1% chance of winnin $100 and X% chance of winning 1000.

Now total revenue for the state = number of tickets sold * price of each ticket = 10,000*5 = $50,000

Now Revenue - Prizes given = State earnings

Prizes given = number of tickets * Expected prize on each ticket = 10,000 ( 10*(0.2) + 100(0.01) + 1000(X) )

State earnings = $10,000 given in the question.

Therefore putting these values we get:

50,000 - 10,000 ( 10*(0.2) + 100(0.01) + 1000(X) ) = 10,000

10,000 ( 10*(0.2) + 100(0.01) + 1000(X) ) = 40,000

Dividing both sides by 10,000 we get:

10*(0.2) + 100(0.01) + 1000(X) = 4

2+1+1000X = 4

1000X = 1

X = 0.001

Therefore the probability of winning $1000 should be kept at 0.001 that is 0.1 %

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