1. Income tax returns. In 2004, the Internal Revenue Service received 312,226,042 individual tax returns. Of these, 12,757,005 reported an adjusted gross income of at least $100,000, and 240,128 reported at least $1 million.27 If you know that a randomly chosen return shows an income of $100,000 or more, what is the conditional probability that the income is at least $1 million?
2. Conditional probabilities and independence. Using the information in Exercise 4.109, answer these questions.
(a) Given that a vehicle is imported, what is the conditional probability that it is a light truck?
(b) Are the events "vehicle is a light truck" and "vehicle is imported" independent? Justify your answer.