A train station has installed a system for determining whether bags contain explosives. It has a 95% chance of correctly identif

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A train station has installed a system for determining whether bags contain explosives. It has a 95% chance of correctly identif

ying a bag containing explosives (5% chance of a false negative), and a 99.5% chance of correctly classifying a bag without explosives as safe (0.5% chance of a false positive). Suppose that the train station screens 4 million bags per year, and that 10 of these bags are expected to contain explosives. (2.5x10-6 probability that a bag contains explosives)A bag is identified by the system as containing explosives. What’s the probability that it actually contains explosives?If we want the probability in part (a) to be at least 0.5, what should the probability of correctly identifying a bag without explosives be?Would it be possible to make the probability in part (a) at least 0.5 by increasing the chance of correctly identifying bags containing explosives? Justify your answerThe probability of identifying a bag with explosives correctly is 95%the probability of identifying a bag without explosives as safe is 99.5%Given a sample space of 4 million, there are 10 bags that are expected to contain explosivesThis is all the info the problem gives me

Mathematics

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PIT_PIT [9.1K] · Answer 1 · 2026-03-18T02:00:46+03:00

a) P(identified as explosive) equals P(actual explosive & identified as explosive) + P(not explosive & identified as explosive) = (10/(4*10^6))*0.95+(1-10/(4*10^6))*0.005 = 0.005002363. Thus, the probability that it actually contains explosives given that it's identified as containing explosives is (10/(4*10^6))*0.95/0.005002363 = 0.000475. b) Let the probability of correctly identifying a bag without explosives be a. Therefore, a = 0.99999763, approximately 99.999763%. c) No, even if this becomes 1, the true proportion of explosives will always be below half of the total detected.