Sports and Leisure An assistant football coach at a Division II school helps his team prepare for the next opponent by charting plays. He looks at game films and records the down distance (first, second, or third down, and a categorical measure of the number of yards needed for a first down) and type of play (rush or pass), to look for tendencies. The two-way table below shows the number of plays that fall into each category. (Fourthdown plays are not charted, because they usually involve a punt or a field-goal attempt.)
Suppose this table represents the true tendencies of the next opponent.
a. What is the probability that the opponent rushes the ball?
b. Suppose the opponent has a first down. What is the probability of a pass?
c. Suppose it is a first or second down. What is the probability that the opponent rushes the ball?
d. Suppose the opponent passes the ball. What is the probability that it is a third down?