MathDB

Two persons,

X

and

Y

, play with a die.

X

wins a game if the outcome is

1

2

;

Y

wins in the other cases. A player wins a match if he wins two consecutive games. For each player determine the probability of winning a match within

5

games. Determine the probabilities of winning in an unlimited number of games. If

X

bets

1

, how much must

Y

bet for the game to be fair ?

45