A pcr test is commonly used for diagnosing a viral infection...

A PCR test is commonly used for diagnosing a viral infection. It has a false positive rate (indicating infection where there is none) of 5% and a false negative rate of 25%. Patients take two tests and if either is positive then an infection is declared. If the actual incidence of the infection is currently two hundred in a hundred thousand, what is the probability that: i) Someone who is declared virus-negative is in fact infected? ii) One or more of ten people tested and allowed on a flight are in fact infected despite screening negative for the virus?

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00:01 In this question, we're given that 0 .5 % of the population is infected with the covid virus and that a covid test gives 3 % false positive and 2 % false negatives.

00:13 Now, we want to draw a 3 diagram first before we answer the question.

00:19 So let's split the event into infected with the virus and the other one is not infected.

00:29 Now we know that 0 .5 % of the population is infected.

00:38 So this means in decimal is 0 .005.

00:42 Now for this branch of the probability tree, i take 1 minus 0 .005.

00:50 I'll get 0 .995.

00:53 Okay, next, we further split the infected into 2 .3, and that is tested positive with the test.

01:06 And the other one is tested negative.

01:12 Same thing for the not infected, for the split no two event, tested positive, and the other one is tested negative.

01:25 Now we know that there's a 3 % force negative, false positive, sorry.

01:31 Force positive means the person is not infected, but tested positive.

01:36 So not infected and tested positive, so it would be here, 3%.

01:40 3 % in decimal is 0 .03.

01:42 So for this part of the probability tree, i take 1 minus 0 .03, i'll get 0 .97.

01:52 Okay.

01:53 Now, 2 % is force negative.

01:58 Now, false negative means the person is actually infected but tested negative.

02:04 Infected, tested negative...

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