Question 729305: I'm new to this site, and in desperate need of help. Will someone give me solutions please?
For Both Problems: Calculate the expected value of lottery, whether it's fair, and if not, determine a price for playing making it fair.
1. Costs you $1.00 to play lottery. You pick 3 digits in order from 0 to 9 (duplicates are allowed). If you win, the prize is $600.00.
2. You pay $1.00 to play lottery. You pick 4 digits in order from 0 to 9 (duplicates allowed). If you win, the prize is $2,000.
Thanks much/
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! 1. The numbers that can be picked go from 000 to 999.
There are 1000 such numbers.
If you play all the numbers at $1 per number, you spend $1000,
and get back $600. The lottery keeps the other $400.
Is that fair?
That is the way lotteries work. They keep a good portion of the money paid for tickets.
On the average that lottery would end up keeping $400 for each $1000 in sales.
From that money, they will pay their expenses, and will have some money left over for whatever the lottery was designed to benefit. Maybe it will be used for subsidized transportation for old people. Maybe it will benefit the poor.
If you wanted to design a lottery like that just to entertain people, a lottery that would not keep any money for expenses or for profits, you would charge $0.60 for the 1 in 1000 chance to win $600.
2. The numbers that can be picked go from 0000 to 9999.
There are 10,000 such numbers.
You have a 1 in 10,000 chance of winning.
It would cost you $10,000 to play all the numbers to be sure to win the $2,000 prize. The lottery would keep $8,000 and give you only $2,000 back.
I would call that most unfair. I never knew of a lottery that kept so much of the money paid for the tickets.
For a 4-digit lottery that returns all the money to the customers, it should cost $0.20 for a 1 in 10,000 chance to win a prize of $2,000.
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