Team A wins five out of six games in a series against team B. Find the maximum likelihood estimator of the probability that team A wins a game against team B. If you were willing to gamble, would it make sense to enter a bet about the next game in the series where you win $1 if team A wins, but lose $6 if team A loses?
Find the likelihood as a function of the binomial proportion p in each of the above case, and find the maximum likelihood.