Hiv blood tests are very accurate around 998 of people with...

HIV blood tests are very accurate: around 99.8% of people with HIV test positive, and 99.99% of people without the virus test negative. In the UK, the prevalence of HIV in adults with no risk factors is around 1 in 10000. For an adult with no risk factors, what is the probability of having HIV given a positive test result? what is the probability of having HIV given a negative test result?

Transcript

00:01 Hi, i'm david and i'm here to help you answer your question.

00:03 Now let me bring up your question here.

00:07 In the question we discuss about the h .i .v.

00:11 And let me try to summarize the question by the three diagram.

00:15 Now at the beginning we have the risk factor is around 1 out of 10 ,000.

00:22 So this will be the hiv.

00:26 So i will put the risk and not rick will be our common.

00:31 Now the risk here will be one out of 10 ,000.

00:37 So if we do one development 10 ,000, get equal to the z -pon -zo -zo -z1 and the common will be the 0 -999 and then the test that will go through the test and the test here it can result in the positive or negative.

01:02 The test will result in the positive and negative here.

01:07 Now for those people that have the hiv and then the test will be accurate to the 99 .8 for people having the test positive, so it will be 0 .998 and it will be negative will be common man 0 .002.

01:30 For those people that they don't have the archivism.

01:32 The test will be negative with the probability 0 .9999.

01:38 So the complement will be 0 .0001.

01:43 So we should form the three diagram.

01:46 Now in the part, i am the question.

01:50 Once you find a doubt with no risk factor.

01:54 So probability that no risk factor will be our complement.

01:59 And then one is the probability that i have an hiv given the positive task result one is a probability of having hiv given the given a positive test result so let me really carefully again for an adult with no risk factor one is the probability of having actually be given a positive task result and then this one will be probability having hiv will be having hiv will be the r and then given them the positive test result given the positive that result would be p that would be that would be the question asking us now by the come by the conditional probability that equal to the r intersection b even by probability of the b now to find the probability of the p it will be here and then we are here as well so it will be 0 .0 .0 .0 .0 .0 .0 .0 .0 .8 plus the 0 .999 plus the 0 .999 times with the 0 .999...

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