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Score: 0/20 0/7 answeredQuestion 6Submit Assessment A certain disease has an incidence rate of 0.99. If the false negative rate Is 79 and the false positive rate is...

Question

Score: 0/20 0/7 answeredQuestion 6Submit Assessment A certain disease has an incidence rate of 0.99. If the false negative rate Is 79 and the false positive rate is 1%, compute the probability that person who tests positive actually has the disease:Give your answer accurate t0 at least decimal placesstart searchR12 G 0 0 *

Score: 0/20 0/7 answered Question 6 Submit Assessment A certain disease has an incidence rate of 0.99. If the false negative rate Is 79 and the false positive rate is 1%, compute the probability that person who tests positive actually has the disease: Give your answer accurate t0 at least decimal places start search R12 G 0 0 *



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$10 \%$ of a certain population suffer from a serious disease. A person suspected of the disease is given two independent tests. Each test makes a correct diagnosis $90 \%$ of the time. The probability that the person really has the illness given that both tests are positive is (A) $0.5$ (B) $0.9$ (C) $0.6$ (D) none of these

In this problem. Let A. B. D. Event that a person has the disease, Person has the disease. And let BBT. The IBT event that I A. Test is positive And I can be either one or 2. Then we have E. Of E. Given us warren drunk be of beer Cuban. Is horns nine. You have beat us be given a part As 1 -7 being given A. It becomes us horned one. Let B. B. D. Once it started as being an intersection b. two before we have feet off B. I. Given A. Because be off leave and given me hindu. We are be to given me it's just 0.81. Are you looking for be given me that is both tests are positive and the person has disease within the best here. Um This is P. Of A. Into the office be given a divided by B. Of A. Into. He asked. We've given you yes be off he brought and two he uh be given abra. How does this whole denominated quantity? This whole it's nothing but to be off really substituting the values. This comes us 0.1 into or indeed one divided by 0.1 into pointed one plus .9 and two .1 and two orange one. So when this comes as 18 by 19 which is point right. The correct option is maybe not

All righty then. In question 38 we see the key words. At least when you see those he words, you know, you're gonna have to use your compliment formula. So my compliment there asking me the probability of a equals one minus the probability of a compliment. The end. So the person tests false positive 0.7 So one minus 10.7 equals my probability of a compliment, which equals 0.993 So now I have one buying this 0.993 raised to the 60th power. I do that. I get a point 34 spring nine and that's my probability at least.

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


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