Find the probability of a prize

[HaLAA]

Homework Statement

The state of Oregon wishes to design a new lottery game with the following rules:  1.Each ticket costs $5  2.There will be three prizes: $10, $100 and $1000  3.The probability of the $10 prize will be 20%.  4.The probability of the $100 prize will be 1%  5.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?

Homework Equations

The Attempt at a Solution

$10000 is the average profit of a month, total income of a month is $50000, total prize of a month is 10*0.2*10000+100*0.01*10000= $30000, this isn't include the 1000 prize

so: 10000=50000-30000-1000*x*10000, x=0.001

can someone check this right or not? Thanks

 

[Orodruin]

Yes, it is correct.