Back pain is a major health problem because of its high prevalence and costs in terms of health care expenditures and lost productivity. Systematic reviews have concluded that chiropractic spinal manipulation appears to be effective in some subgroups of patients with back pain and this is one of the few treatments recommended in clinical-practice guidelines on the care of adults with low back pain in the United States. The effectiveness of physical therapy for back pain has not been well studied, and the results of comparisons of physical 1`therapy with chiropractic manipulation have conflicted. Suppose among a large group of patients with lower back pain, 28% visit both a physical therapist and a chiropractor, whereas 10% visit neither of these. Assume the probability that a patient visits a physical therapist is 0.51. Hint: Start by drawing a Venn diagram.