Tournament

A, B and C are playing in the simple tournament diagrammed at the right.  B and C play first and then the winner plays A. 

Data from past matches give us the following predictions:

If A plays B:                           A will win 70% of the time

If A plays C:                           A will win 80% of the time

If B plays C:                           B will win 60% of the time

Based on these data, calculate the probability A will win the tournament. Use an effective diagram to illustrate your argument.