I'm having some issues with a question from my intro probability course and I'm hoping you can help. Here's the question:
In the World Series in baseball and in the playoffs in the National Basketball Association and the National Hockey Association, the winner is determined by the best of seven games. Most teams have better records at home. Assume that the two teams are evenly matched and each has a 60% chance of winning at home and a 40% chance of winning away. In principle, both teams should have an equal chance of winning a seven game series. Determine which pattern of home games is closer to giving each team a 50% chance of winning. Consider the two common patterns: (a) two home, three away, two home; and (b) two home, two away, one home, one away, one home.
Obviously, If the probabilities stayed the same I could use the binomial distribution and add the probabilities of winning after 4, 5, 6 and 7 games. since they're not, I'm not quite sure how to proceed. Any hints?