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For many​ years, organized crime ran a numbers game that is now run legally by many state governments. The player selects a​ three-digit number from 000 to 999. There are 1000 such numbers. A bet of $ 1 $1 is placed on a​ number, say number 115. If the number is​ selected, the player wins ​$ 300 300. If any other number is​ selected, the player wins nothing. Find the expected value for this game and describe what this means.

 Nov 25, 2016
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Probabilistically:

 

Expected value = p*$300 - (1-p)*$1 where p = 0.001 is the probability of winning.

 

Hence Expected value = $0.3 - $0.999 → -$0.699 or -69.9 cents

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 Nov 25, 2016

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