Higher productivity in the economy usually translates into higher increases in hourly compensation to workers. However, management often delays increasing compensation to show profits for the company. In the data file 'Productivity', for the period 1990 to 2001, productivity is labeled as high for each quarter if the annualized economic growth is at least 2%. In addition, the amount pay increase during the quarter is labeled as large if the hourly compensation is at least 4% on an annualized basis.

a) Suppose that a quarter is randomly selected, what is the probability that this quarter has high productivity growth and has a large pay increase?

b) If a quarter has high productivity, what is the probability that the quarter has a small pay increase?

c) Are the events of productivity and amount of hourly pay increase independent? Explain.