Question 1 You work for a consulting engineering firm who has been contracted by

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Question 1 You work for a consulting engineering firm who has been contracted by the Australian Border Force to evaluate two commercial solutions which are being considered for the next generation border control system. This system utilises iris recognition to verify individuals as they enter the country through international airports. The system employs verification only: a person presents their passport; the system then checks to see if the identity of the person matches the identity of the person named on the passport. This match is conducted by comparing an iris image of the person taken at the border, with the iris image stored on their e-passport. In the border control system, the verification test has two outcomes 1. V+: the person is verified (i.e., their iris image taken at the border matches that stored on their e-passport); or 2. V-: the person is not verified In reality, the person could be: 1. P+: a genuine traveller, who has their own unique and valid passport; or 2. P-: an imposter, who is not genuine and has a fake or stolen passport (for example). Each commercial solution has strengths and weaknesses. The specifications released by the commercial providers are given in the table below. It is also known from historical data that the probability of a person being an imposter is 0.12%. Commercial Solution Selution 1- Eyematch Selution 2- The system correctly verifies a gemuine traveller. 98.26% The system incorrectly verifies an imposter. 5.12% 5.18% la Calculate conditional probabilities Your firm is to compute the conditional probability (for both solutions) that there is an imposter, given the verification is positive; ic. p(P-IV+). Show your calculations using Bayes rule Edit your response to this question here 1b Provide a recommendation Provide your recommendations to the Australian Border Force on the best choice of the solution if th conditional probability ey want to minimise this dit your response to this question here

Explanation / Answer

P(P-)=0.12%

Sol 1:

P(V+|P-) = 1-0.0512 = 0.9488

P(P-|V+) = P(V+|P-).P(P-)/P(V+) = 0.9488*0.0012/(0.9488*0.0012 + 0.9988*0.9826) = 0.001158

Sol 2:

P(V+|P-) = 1-0.0518 0.9482

P(P-|V+) = P(V+|P-).P(P-)/P(V+) = 0.9482*0.0012/(0.9482*0.0012 + 0.9988*0.9835) = 0.001156 < 0.001158

Hence, solution 2 is better as we want to minimize the conditional probability

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