Alice and bob play a series of tic-tac-toe games. alice has a probability of winning of 0.2 in each individual game, while bob wins with a probability of 0.4 in each game, and the probability of a game turning out level is 0.4. the first player to win a game wins the series. find the pmf of the duration of the game. also calculate the probability that alice wins the game. what is the probability that bob wins the game.