Best-of-Seven Probability Question

Hi again,

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.

Re: Best-of-Seven Probability Question

Re: Best-of-Seven Probability Question

Thanks a lot, it is clear now, I forgot to consider the case where B won in 4 and 5 games.