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 Subject: math/statistics/expectations Category: Science > Math Asked by: marine74-ga List Price: \$2.00 Posted: 18 Jun 2005 11:31 PDT Expires: 18 Jul 2005 11:31 PDT Question ID: 534587
 ```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?```
 Subject: Re: math/statistics/expectations Answered By: richard-ga on 19 Jun 2005 13:37 PDT Rated:
 ```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 this 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!```