When Mike is facing a certain pitcher, he knows that 60% of the pitches are fastballs, 30% are curveballs, and the rest are changeups. When this pitcher throws a fastball, it is in the strike zone 75% of the time. Curveballs are in the strike zone 20% of the time and changeups 40% of the time. Randomly select one pitch from this pitcher.

a. Display the provided information using a tree diagram

b. Calculate the probability that the pitch is in the strike zone.

c. Given that a pitch is in the strike zone, what is the probability it is a fastball?