Alice is playing a game In each turn independently of other

Alice is playing a game. In each turn, independently of other turns, she either wins $1, with probability 1=2, or loses $1, with probability 1=2. Initially she has $x, and her goal is to make $(x + y), x; y > 0 integer. The game ends when Alice

Solution

for having x+y $ , she must paly min 3 games ,the chance that she achieves her goal of having $(x + y) at the end of the game= ³C₃(1/2)³

P = 0.125

the expected length of the game = 3