This question was given to me as a review for an upcoming exam:
If a baseball team wins a game, they have a 40% chance of winning the next game due to getting overconfident. If they lose the previous came, there is a 70% they will win the next game. Assume the first game that there is a 50% of winning. What is the probability the team wins the 4th game?
Is there a way to do this without using total probability?
So far I added all of the 8 scenarios that result in a win on the 4th game to get an answer, but I'm thinking there is a way to do this using matrix multiplication instead of total probability.