A fair die is being tossed repeatedly. Alice bets on 2 at every toss, while Ben bets upon 3 and 4 (that is, that either 3 or 4 would be outcome).
(a) Determine the probability that Alice is the first one to win a bet?
(b) Determine the probability that Ben is?
(c) Determine the expected number of tosses until Alice wins a bet?
(d) Determine the expected number of tosses until either Alice or Ben win a bet?