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A person is charged $20 to select one bill. find the expectation. is the game fair?

2007-01-28 03:00:02 · 6 answers · asked by Anonymous in Science & Mathematics Mathematics

6 answers

Well basically, this is like playing poker.

You have 20 bills so you have 20 different possibilities.

10 out those 20 possibilities are $1 - you have a 10/20 chance of getting $1 (or 50%)
5 out of those 20 possibilities are $2 - you have a 5/20 chance of getting $2 (or 25%)
3 out of those 20 possibilities are $5 - you have a 3/20 chance of getting $5 (or 15%)
1 out of 20 of those chances is $10 - you have a 1/20 chance of getting $10 (5%)
and 1 out of 20 of those chances is $100 - you have a 1/20 chance of getting $100 (5%).

You have a 10% chance of breaking even or making a profit. Is it fair? Depends on what you call fair. Many casinos would think this is fair. :)
Personally, I wouldn't waste my money. The "house" has a 90% chance of making a profit.

2007-01-28 03:16:07 · answer #1 · answered by iblori58 2 · 0 2

There are in all 20 bills of which only one ($ 100) has a value more than $ 20. Hence the chance of random drawing this $ 100 bill is just 1/20 or 5%. Thus, if one pays $ 20 for one draw, the game is heavily loaded against the person who pays $ 20.

2007-01-28 03:13:07 · answer #2 · answered by greenhorn 7 · 0 1

Not fair. There are 20 different bills in the box with a total value of $145. If a person made 20 selections it would cost $400 and on average would only get back $145.

2007-01-28 03:10:55 · answer #3 · answered by Anonymous · 2 0

There are twenty bills total. The chances of winning one dollar is 1/2, the chances of winning 2 dollars is 1/4, the chances of winning 5 dollars is 3/20, the chances of winning 10 dollars is 1/20, and the chances for 100 dollars is 1/20.

Thus the expected value is 1(.5)+2(.25)+5(.15)+10(.05)+100(.05)

The equation qives you the answer of 7.25. So you can expect to win 7.25 dollars when playing this game, while the house can expect to win 12.75 everytime someone plays the game, making it unfair

2007-01-28 03:32:45 · answer #4 · answered by Da MC 2 · 3 0

Here's what I think you want:

20 total bills with a total of 145 dollars: so my expectation is $7.25
And no the game is not fair.

For every $20 played you would lose $12.75.

2007-01-28 03:20:03 · answer #5 · answered by Richard 7 · 3 0

the expectation is the 100 bill

2007-01-28 03:13:39 · answer #6 · answered by Anonymous · 0 1

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