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Certaln disease has an incidence rate f 0.6%_ If the false negative rate Is 87 and the false positive rate Is 3% , compute the probability that person who tests po...

Question

Certaln disease has an incidence rate f 0.6%_ If the false negative rate Is 87 and the false positive rate Is 3% , compute the probability that person who tests posItive actually has the disease_ Leave your answer In decimal form; do not convert It t0 percent.Glve your answer accurateleast dccimal places

certaln disease has an incidence rate f 0.6%_ If the false negative rate Is 87 and the false positive rate Is 3% , compute the probability that person who tests posItive actually has the disease_ Leave your answer In decimal form; do not convert It t0 percent. Glve your answer accurate least dccimal places



Answers

HIV Testing A particular test for HIV, the virus that causes AIDS, is 0.7$\%$ likely to produce a false positive result-a result
indicating that the human subject has HIV when in fact the person is not carrying the virus. If 60 individuals who are HIV-negative are tested, what is the probability of obtaining at least one false result?

So he questioned 38. We're looking to find the probability of at least one balls results. So when we see those words, at least we know we're gonna be using our complement wool. So we're finding the probability of a equals one minus the probability of a compliment. The end power, at least one. Oh, so we have equals one minus. So now, my and see, my confidence is one minus 10.7 So this is 0.993 raised to the safety of our and that's been equal white three for three, no.

So this one says, assumed that zero point one percent of the population off the United States has a certain deceits. I assumed that assume further, that there is a test for this disease that is ninety nine percent accurate. This means that ninety nine percent of the people who have the disease will test positive and one percent of the people who have a disease. Will Iranian Cicely test negative? Similarly, ninety nine percent of the people who do not have a disease, what has negative and one percent of the people who do not have the disease? Will Iranian slee test positive? In two thousand fifteen, one million people were given this test. What percent of the people who tested positive actually had the disease? So then we can start by saying what? The disease of flicks zero point one percent of the population which is going to be zero point zero zero one. So they are the one million people tested a million. You can multiply that by zero point zero zero one and see that that would be one thousand people. So then one thousand people had the disease god disease, which means that the other one million minus the people who have the disease will be the nine hundred ninety nine thousand people that don't have to the disease. Okay, so then from there, out of the people that do have the disease, we know that nine ninety nine percent of them tested positive. So out of the one thousand ninety nine percent tested positive on, then that's gonna be the nine hundred and ninety people. And then, which means the other time are going to have tested negative, even if they did have a disease. So then I had the people that don't have a disease. We know that out of the nine hundred ninety nine thousand, ninety nine percent of the people I'm tested negative, like they're supposed to, which is going to be the nine hundred and eighty nine thousand and ten testing negative like they're supposed to on. Then let me see. The one percent of the nine hundred ninety nine thousand are gonna accidentally test positive, as if they did have it. The disease, even if they don't have the disease. So that one percent is gonna be the nine thousand nine hundred and ninety of them. So then, if We're looking for the total people that tested positive. It's going to be the number which is going to be the nine thousand nine hundred ninety. So this number right here, Elin, this number plus nine ninety, which is going to be ten thousand. No, I had an eighty them out of that. So we know that out of the people that tested positive, which we can put in the denominator. So these are the people that people that tested positive regardless of people that tested, regardless of if they actually had the disease or not. This is just talking about like the test. Then we know that we can divide the people that actually had it and tested positive, which is ninety. And if we do that, we know that that gives us nine percent. So then that means that even though the test is ninety nine percent accurate, nine percent of the people who tested positive for the disease actually hot it. So there's so many. There's so many people that are actually walking around thinking that they have this disease who don't actually have the disease, just kind of a big number

Okay. First we have the problem. I indicates those riches infected p represents tested as you are A It'll be probably high equal your ability he given. I think your 0.9 p giving I compliment traded i e Because people to probably p I probably divided by the probability given I cross probably here. You're I come here. I e here. Thank you. Very. Which is people stare appointments heroes eat divided by 1616 It'll keep probably I popular treat you pull toe Serkan, feel very your point. Thank you. Bye bye. Here 0.0.98 theory here. You know your 9 to 0 30.3 is the probably given I company probably thinks is also equivalent to one minus the probability I given p So then now calculates because he called to should be called Teoh 69 use by then. For Prince Dude, probably I live in peace. Complementary which is supposed to be physicals. 19 is your 190.106 Multiple five. But I wonder if I buy this mobile. It easier points you You multiply by your opponent zero e v which is equal by 18,235. Never buy Diva doing Probably I complementary given complimentary, which is probably high getting peed Compliment Religion People 2 to 2281 divided by 2232 130 35.

Okay. So objective here is determined the probability that someone who test positive has the disease. So this is part A, um Well, I'm gonna use the famous Bayes theory. Almost. The probability of F given e is equal to the probability of e give enough times the probability of f all divided, all divided by the probability of e given f times the probability of f plus the probability of e given f compliment times the probability of f compliment. So we just plug in, um, the values here into this formula, and we have what we have. Zero point 999 um, times 0.1 divided by 0.999 times 0.1 plus Yeah. Um, 0.2 times 0.9999 Okay, this is going to give us, uh, she looks out. Here. We get I believe it. 0.0 99 divided by 0.29988 which is gonna be equal to? Let's see here. 0.3331 332533 Okay, so therefore is approximately. We could round this to, let's say, 0.333 Right. There's approximately a 0.333 or bought a 33.3% chance off having the disease. Um, even if the test positive as, um, the disease is very rare. Okay, um and then part B well, objective here is to determine the probability that someone who tests negative has the disease. Okay, well, using, um, based them again, we can get the probability now off. F compliment given e compliment is equal to the probability off e compliment given f compliment times the probability of, um, f compliment all divided by the probability of the compliment given f compliment times the probability of enough compliment plus the probability of e compliment given f compliment times Thebe Probability of f. Okay, well, okay. Um so, um, again and plug in the values here we get to the probability of f compliment given e compliment is going to be equal to Well, um, Let's see here. 0.998 times 0.999 Divided by 0.9998 times 0.9999 plus 0101 time 0.1 Um, which is gonna be really close to 0.9999 99 and then from zeros. Um, so we can say here there's gonna be approximately a 0.999 or 99.9% chance off not having the disease, even if, um, because positive did you?


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