In the Blade Runner universe, replicants are bioengineeredandroids that are virtually identical to humans. The“Voight-Kampff” test is designed to distinguish replicants fromhumans based on their emotional response to test questions. Thetest designers guarantee an accuracy rate of 90%. In other words,they guarantee that if a replicant is subjected to the test, thenthe test will correctly label them as a replicant with probabilityq = 90%. With the remaining probability, the test incorrectlylabels the replicant as a human. Similarly, if a human is subjectedto the test, then they will be correctly labelled as human withprobability q = 90%, and with the remaining probability they willbe incorrectly labelled as a replicant. A subject, Leon, issuspected to be a replicant. Your prior probability that Leon is areplicant equals p = 75% and with the remaining probability 1 ? p =25% you suspect Leon is a human. (a) What is the probability thatif Leon takes the Voight-Kampff test, the test will label him as areplicant? (b) Leon is subjected to the Voight-Kampff test, and thetest labels Leon as a replicant. What is your posterior probabilityabout whether Leon is a replicant or not? (c) Another subject,Deckard, is also suspected to be a replicant, and your priorprobability is that Deckard is a replicant with probability p1 =10% and human with probability 1 ? p1 = 90%. Deckard takes thetest, and is labelled as a human. What is your posteriorprobability about Deckard?
