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The individual actually had the disease Yes Ho Positive 120 Negative 121...

Question

The individual actually had the disease Yes Ho Positive 120 Negative 121

The individual actually had the disease Yes Ho Positive 120 Negative 121



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Suppose that one person in $10,000$ people has a rare genetic disease. There is an excellent test for the disease; 99.9$\%$ of people with the disease test positive and only 0.02$\%$ who do not have the disease test positive.
a) What is the probability that someone who tests positive has the genetic disease?
b) What is the probability that someone who tests negative does not have the disease?

Hello everyone. So we'll be going to solve problems 1 20 from chapter two, probability In this question. It is given that there is a rare disease that is existing. And the probability of having their diseases one out of 500. So probability of have diseases one out of 500. That is 0.00 two. Now it is given that if the test is being taken, not always the positive gives positive results and negative gives negative result. So what they're given that's if the person has the disease, the chances of positive result piece transfer, positive result. Yes. since 0.9 fight. So 95% of the times the correctly diseases identified. Yeah. Similarly reliability of positive result given that the person doesn't have the disease did not Has given us 0.0. What now we have to calculate It is given that a person which is randomly selected that he has the disease. This being they stood positive. The result shows that he has the disease. Now we have to tell what is the probability that he actually has the disease. So this will eventually become we will use the beasts tool two calculators at the bottom. The total sum of viability has come. Yeah. What do you play by? Probably not. Yes. We have considered both the scenarios. We will just input the values. We have already calculated this. Fell p 0.95. We have greater number Will be will be 0.00 two. This value will be same. VD dash will be one minus 0.002. Really good person doesn't have the disease. So we have used this value. We'll just be solving the situation now to get our final result. This will be 0.00 one night. Yes. This will become 0.00998. And when we calculate this Final answer isn't calculator. Final answer will be 1 0.15. Right. Right. So this is the probability. But we had to find out. You have to find out if a person has tested positive. What were the property that he actually has the disease? So this will be 0.15 99 Thank you.

So here we are, considering one patient that has been completely cured of AIDS or completely been cured from any sign of HIV inside their body. So here you can imagine that the individual with AIDS is going to have multiple T helper cells infected by the HIV virus. This individual also happened to have leukemia, which is basically a cancer of blood cells. Specifically white blood cells such as, say, neutrophils, other lymphocytes or other granular sites inside the body. And one of the possible therapies to treat leukemia is something called a bone marrow transplant. So bone marrow transplants can be very risky, and they basically involve irradiation of all the white blood cells inside an individual's body and replacing them with bone marrow and other white blood cells from a donor. So here, in this case, you can imagine that many of the T helper cells, as well as many of the other white blood cells inside this infected individuals body were eliminated through this irradiation process. Of course, you will also have some strands and viruses of HIV inside the bloodstream. However, this white blood cell, or bone marrow donor also happened to have the mutation that prevented them from contracting HIV, So it was an HIV resistant donor. So here this white blood cell or bone marrow donor had t help ourselves that they were giving to the individual that had protection from entrance of the HIV virus. So here, this individual that got this bone marrow transplant was effectively cared of both AIDS because he could not be infected by the HIV virus left inside his body. And he no longer had leukemia due to the eradication of the cancerous white blood cells in his body. By this irradiation. So here, by the end, the individual had normal white blood cells as well as normal T help ourselves and the source that each of these components come from the T cells and white blood cells would come from that donor bone marrow. So they no longer had any chance of generating these infected T helper cells or any of the cancerous white blood cells in the first place. So here they are, effectively cured of the AIDS virus. So the advantage of this is it's an actual parable option. However, due to the riskiness of the bone marrow transplant, MM, low occurrence of the HIV resistant mutation, especially in a compatible bone marrow transplant. Donor believes this option to be very limited and very unusable in public circumstances, So this is pretty much a one individual circumstance that may not be seen again in the future unless further expanded on by research or other scientific discoveries in the future.

In this problem. Let it be the event that person has disease and B. I. B. The event right? The riot test yes positive. I can be one two. We have E. As 0.1 B. B. A. Given A as 0.9 be be given you're nice as one minus B. Being given A. Which is .1. No let bebe Equal to be even intersection b. two to be given A. Is B. Be even given me into P. Be too given A. Which is .9 in 2.9 which is .81. The the E. Dash is 0.1 into horned one. Therefore we have be given B from the beast terrible spear into be given a demanded by B. B. Which is so be it just be A into B vigorously. Yes the A dash into the region A dash substituting the values this is .1 and do 0.81 surrounded by 0.1 into .81 plus 19 into .1 in 2.1. Following this we get this as it even by 90 Which is nine by damages .9 the correct option ist me

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


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