# Probability of a dice game: win, lose or draw.

$C$ and $J$ play a game. $C$ always starts. $C$ rolls a fair dice first and wins if he throws an even number. If not, then $J$ rolls the dice. If she rolls an odd number she wins. if neither win it's a draw. a) What is the probability of the game being drawn? b) Is this game fair? If they played the game $100$ times how many games should $J$ win?

• What have you tried? Note that these rolls are just like flipping a coin, as even and odd each have probablity $1/2$ There are only three possible outcomes, so write them all down and assess the probabilities. – Ross Millikan May 20 '15 at 21:48

Hint: If the game was fair then the probability that $J$ wins should be $1/2$, since that is the probability that $C$ wins. But a draw is possible. This can also help you figure out the last part of the problem.
a) The probability of a draw is simply that C rolls an odd number and J rolls an even number, i.e. it is $0.5\cdot0.5=0.25$.