Probability Math Question!

Question

Hi, I have this probability question that involves a tree diagram. I have some of it done but am stuck on the percentages that should go on each branch. If you could include the steps and everything to how you got the answer so I can check and make sure that what I have is right, that'd be great!

 

Suppose the Atlanta Braves are playing the Pittsburgh Pirates in the World Series (7 games). So far the
Pirates have won 2 games, and the Braves have won one. If the odds for either team to win any game
are even and the series ends when one team wins four games, what is the probability that the Pirates
will win the Series?

 

Thank you!!

Answer 1

Anna, here are two generalizations that may help:

* each branch has the probability 1/2

* each complete path to a win has the probability of (1/2) to the power of the length of the path. That is, if there are only two more games, the probability of the path is (1/2) to the power 2, or 1/4

now here are the remaining paths

BBB
BBPB
BBPP
BPBB
BPBP
BPP
PBBB
PBBP
PBP
PP

Now write down the path probability next to the path, add up the ones that end in P.