The doping example lays out the logical steps necessary to get to the quantity that is really of interest when making decisions: out of people who test positive, the proportion who are really doping, which turns out to be 19/68. The expected frequency tree shows that this depends on three crucial numbers: the proportion of athletes who are doping (1/50, or 20/1,000 in the tree), the proportion of doping athletes who correctly test positive (95%, or 19/20 in the tree) and the proportion of non-doping athletes who incorrectly test positive (5%, or 49/980 in the tree).
