Imagine a hypothetical country of 100 million ruled by a ruthless dictator bent on suppressing opposition. The opposition is estimated at 1000 individuals, all living in exile. The dictatorship is using a highly sophisticated voice-recognition wiretapping system that will alert the country’s security apparatus of the whereabouts (GPS, if you will!) of any opposition member infiltrating the country, resulting in near certain apprehension. The wiretapping system is 99% accurate in recognizing the voice of a true opposition member. On the other hand, there is a 5% chance that an innocent citizen is misidentified by the system.

(a) Estimate the number of innocent citizen likely to be apprehended.

(b) Determine the probability that a true infiltrator is apprehended.

(c) Comment on the effectiveness of the system in meeting the dictatorship goal of suppressing opposition.