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

Question

$C$ 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?

Answer 1

a) The probability of a draw is simply that C rolls an odd number and J rolls an even number, i.e. it is $0.5\cdot0.5=0.25$.

Answer 2

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.