A 1981 retrospective study published in the prestigious New England Journal of Medicine looked at the use of cigars, pipes, cigarettes, alcohol, tea, and coffee by patients with pancreatic cancer and concluded that there was “a strong association between coffee consumption and pancreatic cancer” [17]. This study was immediately criticized on several grounds, including the conduct of a fishing expedition in which multiple tests were conducted and the most statistically significant result reported.

Subsequent studies failed to confirm an association between coffee drinking and pancreatic cancer [18]. Suppose that six independent tests are conducted, in each case involving a product that is, in fact, unrelated to pancreatic cancer. What is the probability that at least one of these tests will find an association that is statistically significant at the 5 percent level?