As the current opioid epidemic highlights the increasing injection drug use in rural communities, the relationship of injection drug use and its infectious disease consequences are of increasing interest. In communities with large HIV outbreaks, a heavy majority of recent HIV diagnosis were also diagnosed with hepatitis C. Suppose among a rural community in Ohio, 33% were diagnosed with both HIV and hepatitis C, whereas 40% had neither of these. The probability that someone was diagnosed with HIV is 0.41.

What is the probability that a randomly chosen person in this community was diagnosed with hepatitis C? What is the probability that a randomly chosen community member is diagnosed with HCV given that s/he does not have HIV? Are the events of being diagnosed with HIV and hepatitis C mutually exclusive?