I am struggling once again (no surprise) with calculating probabilities...
Two baseball games play a best-of-seven series in which the series ends as soon as one team wins four games. The first two games are played on A's field, the next 3 on B's and the last 2 on A's. Given that the probability A wins on their home field is 0.7, and on B's field is 0.5, what is the probability the series does not go to 6 games?
I have that the probability they in in 4 is 0.1225, and 5 games is 0.175... Are these in any way related to the answer?
I have thought about calculating the probability that the game goes to and taking the complement of that, but that would not include the series that went to 7 games. Kind of unsure where to piece this info together. Any insight would be much appreciated.
Thanks in advance.