# 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 This solution is **FREE** courtesy of BrainMass!

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 (x=4,y=6 or x=5,y=5 or x=6,y=4) out of 36 (the total number of outcomes when you roll 2 dice).

b) From the same reason we have P(x+y=7)=6/36 and P(x+y=11)=2/36

Therefore P(x+y is neither 7 nor 11)=1-P(x+y=7)-P(x+y=11)=1-6/36-2/36=28/36

c) In part a) your chances to win are 3/36 and your chances to loose are 1-3/36=33/36.

So to loose there are 11 times more chances to loose than to win.(compare 33/36 to 3/36)

So in order the game to be fair, if you bet 1 dollar, if you win the house should pay you 11 dollars plus your dollar.

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