• Not so simple:

    An 18th century concept in statistics, known as Bayes’s theorem, can help us. This theorem tells us how to calculate the probability of an event given that another event has happened. For example, say people in a particular colony are being tested, and 20% of them actually have the disease. Next, say the sensitivity (probability of a positive result given the disease is present) of the test being used is 80% and its specificity (probability of a negative test result given the disease is not present) is 90%. A little bit of math yields the following probabilities:

    True positive = 0.16
    False positive = 0.08
    False negative = 0.04
    True negative = 0.72

    According to Bayes’s theorem, the probability that the disease is present given a negative test result can be obtained by multiplying the probability of disease in the locality (0.20) and the probability of a negative result given the disease is present (0.20), then dividing this by the probability of a negative test result (0.76). This value comes out to be 5.26%. That is, a little more than 1 in 20 people who test negative may actually have the disease. Similarly, the probability of ‘no disease’ given a positive test result is 33.3%.

    If the disease’s prevalence in the colony rises to 50%, these two figures become 18.2% and 11.1%, respectively. If the prevalence increases to 80%, these figures become 47.1% and 3%, respectively.

    From here: https://science.thewire.in/the-sciences/covid-19-rt-pcr-serological-tests-false-positive-false-negative-rate-bayes-theorem/

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