Problem using Bayes theorem
Two baseball teams, the Toronto Jaybirds and the Philadelphia Cheesesteaks, are members of a fictitious baseball league. Whenever two teams in this league face each other, they play a series of up to five games. The first team to win three games wins the series; any remaining games are not played. There are no tied games; every game will continue until one team wins. All games in a given series will be played on the same field. Just before the start of a series, the location of the series (either Toronto or Philadelphia) is determined by a single random coin flip. The Jaybirds have managed to sneak in a biased coin this year, so they will win the coin toss (and play the series in Toronto) with probability 3/5. Baseball experts predict that the Jaybirds will win any game played in Toronto with probability 5/8 and any game played in Philadelphia with probability 1/2. Consider a series whose location you do not know. i. Given that the Cheesesteaks win the first two games, what is the probability that the series is in Philadelphia? ii. Given that a game five is about to be played, what is the probability that the series is in Toronto?