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?
a) Let x=number of points on the first die and
y=number of points on the second die.
since we have 3 wining possibilities for x+y=10 ...
Probabilities of dice rolls are determined, as well as payoff information if one was gambling on an outcome.