Data were obtained on the incidence of rheumatic disease and the presence of grimacing in schizophrenic patients. In a sample of 1,942 patients, 6% had a known history of rheumatic disease, 21.8% grimaced, and 1.8% had a history of both rheumatic disease and grimacing. Fill in the table below with the appropriate probabilities
a. What is the probability that the patient grimaces?
b. What is the probability that the patient has a history of rheumatic disease?
c. What is the probability that the patient grimaces given that he or she has a history of rheumatic disease?
d. Are grimacing and rheumatic disease statistically independent? Explain.