Many sports leagues decide their champions using a best-of-seven format (e.g., the MLB, NBA, NFL, etc.) There is a Team A and a Team B. The two teams play each other for at most seven games. The first team that wins 4 games is declared the winner. Assume that the games are in dependent of each other.
Suppose Team A is the better team and has a $60\%$ chance of winning each game.
a. What is the probability that Team A will win the championship in $7$ games?
b. What is the probability that Team A will win the championship?
I think that for part A it is $(4/10)^6 \cdot (6/10)$ because that would mean they win on the 7th game, but I'm not sure if that's what it is asking for. And for Part B wouldn't it just be $60\%$?
Any help would be nice, thank you!