if a gambler rolls two dice and gets a sum of 10, he wins $10.00, and
if he gets a sum of three, he wins $20.00. The cost to play the game
is $5.00. what is the expectation of this game?

Hello and thank you for your question:

To get a sum of 10 you need one of
6+4
4+6
5+5

To get a sum of 3 you need one of
2+1
1+2

In all there are 36 possible outcomes (6 choices from each die)

So 3/36 of the time he gets $10
$10*3/36= 0.833333333

and 2/36 of the time he gets $20
$20*2/36= 1.11111111

That adds up to $1.94444444
So the expected return is 1.94444444- 5.00 = -$3.05555556 or -$3.06 if you round

I did it myself, but I also found the same question answered (for $1.99) at
http://askearth.com/go/view_request?request=101315

Richard-ga

I don't think that's correct, actually. =/

You have to multiply the probability for each outcome by the change.

There is a 3/36 chance to win $10, or .8333

There is a 2/36 chance to win $20, or 1.111

There is a 31/36 chance to lose $5, or -4.305

You add up the probablility of each case, and you get an expected value of

  -2.361

instead.

You can check out <A
HREF="http://en.wikipedia.org/wiki/Expected_value">this</a> for
further reference.

I stand by my answer - - win or lose, you pay the $5.00 100% of the time.

Whoops... I misread it I didn't realize that you didn't get the $5 back.


Touche!