What do you think?

Leonard Mlodinow, author of the book The Drunkard 's Walk: How Randomness Rules Our Lives, tested positive for HIV and was told by his doctor that he had a 99% chance of actually having HIV. However, his doctor had fallen victim to the "confusion of the inverse" and given him the probability that a patient tests positive for HIV given that they actually have it, not the (much smaller) probability that a patient actually has HIV given that they test positive for it. Mlodinow effectively put his life on hold for a year until further tests revealed that he did not have HIV. Give two further examples of situations in which the "confusion of the inverse" (also known as the "prosecutor's fallacy") can cause problems. (Note: Simply replacing "HIV" with the name of another medical condition does not count as a further example.)