In a physician practice, 20% of patients are male and 80% are female. You have noted that 6% of the male patients come to an appointment for a routine physical with prepared written questions, but only 3% of the female patients bring written questions to their appointments. In this problem, use the notation: M for male patient, F for female patient, Q for brings written questions to physical appointment and NQ for does not bring written questions to appointment. State the information given in the problem, using the correct notation. Draw the probability tree, with labels, and the joint probability tree for this problem. Calculate the following, showing your work, and including the notation for the event:
a. Probability that a patient brings written questions and is male.
b. Probability that a patient brings written queqstions.
c. If a patient brings written questions, the probability that patient is male.
d. Are gender and whether a patient brings written questions independent? Why?