In three careful studies [21], lie detector experts examined several persons, some known to be truthful and others known to be lying, to see if the experts could tell which were which. Overall, 83 percent of the liars were pronounced “deceptive”

and 57 percent of the truthful people were judged “honest.” Using these data and assuming that 80 percent of the people tested are truthful and 20 percent are lying, what is the probability that a person pronounced “deceptive” is in fact truthful? What is the probability that a person judged “honest” is in fact lying? How would these two probabilities be altered if half of the people tested are truthful and half are lying?