# Probability : Dice and Payoff

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?

https://brainmass.com/math/probability/probability-dice-payoff-10292

#### 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 ...

#### Solution Summary

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

$2.19