Is age category independent of willingness to try new products? According to the US Census Bureau, approximately 20% of all Americans are in the 45–64 age category. Suppose 24% of the consumers who purchased Total for the fi rst time during the initial 10-month period were in the 45–64 age category. Use this information to determine whether age is independent of the initial purchase of Total during the introductory time period. Explain your answer.

#!#1.3 Using the probabilities given in Question 2, calculate the probability that a randomly selected US consumer is either in the 45–64 age category or purchased Total during the initial 10-month period. What is the probability that a randomly selected person purchased Total in the fi rst 10 months given that the person is in the 45–64 age category?