![]() ![]() They are actually on drugs? So let's look at the first part. Given that the applicant tests positive, what is the probability that You could say this is 9,310 over 10,000 or you can multiply by the path on our probability tree here. ![]() ![]() What percent is 9.310? Well that is going to be 93.10%. It by 190 over 10,000 or you could just say two Original applicant pool is this? Well 190 is 1.9%, and we could calculate The other 98%, so 9,500 minus 190, that's gonna be 9,310 willĬorrectly test negative. So they are testing positive, and then the other 98% willĬorrectly come out negative. What's two percent of 9,500? It's 190 would test positive even though they're not on drugs. So two percent are going to test positive. And this is where the false positive rate is going to come into effect. If you take five percentĪnd multiply by 99%, you're going to get 4.95%. If you take five percentĪnd multiply by one percent, you're goin to get 0.05%. Well this is gonna be five out of 10,000. Tests negative for drugs? The test says that hey Original applicant pool that is on drugs but Our original applicant pool is on drugs and tests positive, well 495 over 10,000. And then we're going to have one percent, which is five, are going to test negative. So what is 99% of 500? Well let's see, that would be 495. To get the correct result in that they're going to test positive. Has a false negative rate of one percent. Result for some of them, and we know that because it It would say positive for all of them, but we know that it's not a perfect test. Happen when we administer the test to the people who are on drugs? Well the test, ideally, And then how many are not on drugs? Well 9,500 not on drugs. So what's five percent of 10,000? So that would be 500. So five percent are actually on the drugs, 95% are not on the drugs. So we can immediatelyīreak this 10,000 group into the ones that are doing the drugs and the ones that are not. Of all their applicants are actually using illegal drugs. Now they give us someĬrucial information here. This is also going to beġ00% of the applicants. It's easy to do the math better than saying 9,785. It could have been 100,000, but I like this number 'cause I will both talk in absolute numbers, and I just made this number up. ![]() It's fairly straightforward to do the mathematics. Number of applicants, and I'll use a number where To conceptualize is just, let's just make up a large Percent of all their applicants are actually using illegal drugs. It is falsely giving a negative result when it should have given a positive one. Take the illegal drugs, it'll say that they didn't. What does that mean? That means that one percent of the time if someone did actually If someone did not do drugsĪnd you take this test, there's a two percent chance saying that you did do the illegal drugs. It should have read negativeīut it read positive. Percent of the cases, when it should have read negative, that the person didn't do the drugs, it actually read positive. What does that mean? That means that in two So there is this drug testįor the job applicants and then the test has a false So first let's make sure we understand what they're telling us. They are actually on drugs? So let's work through this together. Giving the applicant test positive, what is the probability that Of all their applicants are actually using illegal drugs and we randomly select an applicant. Has a false positive rate of two percent and a false Screens job applicants for illegal drug use at a certain stage in their hiring process. ![]()
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