Question: (15pts) A personnel manager has constructed the following table to define nine combinations of talent and motivation. The numbers in the table are based on the manager’s estimates of the probabilities that an applicant for a managerial position in her firm will be classified in the respective categories.

a) What is the probability that a new applicant will have low talent?

b) What is the probability that a new applicant will have medium motivation and low talent?

c) What is the probability that a new applicant with medium motivation will have low talent?

d) Are talent and motivation statistically independent? Explain carefully.