Asked by Rose

Suppose that the SJCS and Mary Ward are in the basketball final. In this best-of-three series, the winner is the first team to win two games. There are 60% chances SJCS TEAM will win first game. If SJCS wins, there are a 70% chance of winning next game and if they lose there are 45% chances of winning next game.
Create a tree diagram and find the probability for each case
Find the probability of SJCS win the series

I really don't understand how to draw the diagram... And finding the probability of them winning. Please help
Answered by Reiny
Not possible to show tree diagram here, but I would start a tree for each school
with two branches whose endpoints would be W and L (for win and lose)

From the W end, I need two more branches, again labeled W and L
Do the same for the L end, etc until a series of branches has 2 W's

Suppose we look at the SJCS branches
they can win along the following branches:
WW -->(.6)(.7) = .42
WLW --> (.6)(.3)(.45) = .081
LWW --> (.4)(.45)(.7) = .126

prob(SJCS wins) = .42 + .081 + .126 = .627
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