The paper “Predictors of Complementary Therapy Use Among Asthma Patients: Results of a Primary Care Survey” (Health and Social Care in the Community [2008]: 155– 164) described a study in which each person in a large sample of asthma patients responded to two questions:
Question 1: Do conventional asthma medications usually help your symptoms?
Question 2: Do you use complementary therapies (such as herbs, acupuncture, aroma therapy) in the treatment of your asthma? Suppose that this sample is representative of asthma patients. Consider the following events: E = event that the patient uses complementary therapies F = event that the patient reports conventional medications usually help
The data from the sample were used to estimate the following probabilities: P(E) = 0.146 P(F) = 0.879 P(E ∩ F) = 0.122
a. Use the given probability information to set up a “hypothetical 1000” table with columns corresponding to E and not E and rows corresponding to F and not F.
b. Use the table from Part (a) to find the following probabilities:
i. The probability that an asthma patient responds that conventional medications do not help and that patient uses complementary therapies.
ii. The probability that an asthma patient responds that conventional medications do not help and that patient does not use complementary therapies.
iii. The probability that an asthma patient responds that conventional medications usually help or the patient uses complementary therapies.
c. Are the events E and F independent? Explain.