A corporation was concerned about the basic educational skills of its workers and decided to offer a selected group of them separate classes in reading and practical mathematics. Forty percent of these workers signed up for the reading classes, and 50% for the practical mathematics classes. Of those signing up for the reading classes, 30% signed up for the mathematics classes.

(a) What is the probability that a randomly selected worker signed up for both classes?

(b) What is the probability that a randomly selected worker who signed up for the mathe- matics classes also signed up for the reading classes?

(c) What is the probability that a randomly chosen worker signed up for at least one of these two classes?

(d) Are the events "Signs up for reading classes" and "Signs up for mathematics classes" statistically independent?