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# Probability : Dice and Payoff

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Suppose you roll two dice
a) What are the odds in favor of rolling a sum of 10?
b) What are the odds against rolling a sum of 7 or 11?
c) In part a, if you bet one dollar that a sum of 10 will turn up, what should the house pay (plus returning your one dollar bet) if a sum of 10 turns up for the game to be fair?

##### Solution Summary

Probabilities of dice rolls are determined, as well as payoff information if one was gambling on an outcome.

##### Solution Preview

a) Let x=number of points on the first die and
y=number of points on the second die.

Then P(x+y=10)=3/36=1/12
since we have 3 wining possibilities for x+y=10 ...

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• BSc, University of Bucharest
• MSc, Ovidius
• MSc, Stony Brook
• PhD (IP), Stony Brook
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