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Numerade Educator

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Problem 75 Medium Difficulty

There has been a great deal of controversy over the last several years regarding what types of surveillance are appropriate to prevent terrorism. Suppose a particular surveillance system has a
99$\%$ chance of correctly identifying a future terrorist and a 99$\%$ chance of correctly identifying someone who is not a future terrorist. Imagine there are 1000 future terrorists in a population of 300 million (roughly the US population). If one of these 300 million people is randomly selected and the system determines him/her to be a future terrorist, what is the probability the system is correct? Does your answer make you uneasy about using the surveillance system? Explain.

Answer

.00329

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Video Transcript

all right, we're giving the system that's supposed to prevent terrorism by just surveillance. So we're giving that it has a 99% chance of correctly identifying a future terrorists. So let's set some variables. Why equals the event that we get a positive reading? Let's just phrase that as the event of a positive reading, uh, positive reading just for concession and see equal the event a subject is the future terrorist. All right, we're given that the probability, given the subjects of terrorists to get a correct reading, a positive reading that 0.99 were also given that the probability of correctly I didn't find somebody is not a terrorist is 0.999 99.9%. So the probability of not getting a positive reading given that the subject is not a terrorist zero point 999 were given that in the sample 1000 of these people future terrorists 300 million, which I'm just gonna abbreviate like that. What is the probability that given we get a positive reading, that person is a terrorist? And for that we're just going to use some base there, so scums p t times p. Y t. Why given t my fault. Then over this note, that should be a plus. Now we have all these variables. We just need to take the compliment of a few things. So sorry. This Just say pft not t equals. So therefore p of t prime r t compliment or not tea or whatever you wanna call this one minus 1000 or 300 mil and P. Why not? Tea equals 0.11 So we plug all that in yet 1000 300 mil times 7.99 all over 100 Sorry. 1000 over 300 mil times 0.99 plus one minus 1000 with 300 mil times 0.1 If you do the math, this turns out to be 0.32 ish, which is 0.32% now. I can't answer the second part of this question for you because that's an opinion question. But make of that data, what you will is what I'll say