Every month 100 million people fly on commercial airlines. Imagine 10 of them are potential terrorists.

Airport security are able to correctly identify that a person is a terrorist in 99% of cases and a non-terrorist in 99.9% of cases.

a) A person is identified by airport security as a terrorist. What is the probability that they are a terrorist? [2 marks]

b) Intuitive responses to questions of this type tend to involve much higher probabilities. Discuss how intuitive responses could err due to: i) confusion of conditional probabilities or ii) people placing the same probability on all possible hypotheses (uniform priors). [2 marks]