A particular football team is known to run 30% of its plays to the left and 70% to the right. A linebacker on an opposing team notes that the right guard shifts his stance most of the time (80%) when plays go to the right and that he uses a balanced stance the remainder of the time. When plays go to the left, the guard takes a balanced stance 90% of the time and the shift stance the remaining 10%. On a particular play, the linebacker notes that the guard takes a balanced stance.
a. What is the probability that the play will go to the left?
b. What is the probability that the play will go to the right?
c. If you were the linebacker, which direction would you prepare to defend if you saw the balanced stance?