Rapid tests for Covid tend to have very few false positives, but a relatively large number of false negatives. For a particular rapid test, if someone has Covid, there is a 65 percent chance they will test positive, and if the person does not have Covid, there is a 99.9 percent chance they will test negative. Suppose that 5 percent of the population has Covid. If someone tests negative using a rapid test, what is the probability that they do not have Covid?

The question is asking for the probability that a person does not have Covid given that they tested negative (also known as the posterior probability). In order to find this, we can use Bayes' Theorem which provides a way to revise existing predictions or theories (in this case the 5% prevalence of Covid) given new or additional evidence (in this case the negative test result).

The formula for Bayes' Theorem is:

P(A|B) = [P(B|A) * P(A)] / P(B)

Where,
P(A|B) is the probability of A given that B has occurred,
P(B|A) is the probability of B given that A has occurred,
P(A) and P(B) are the probabilities of A and B regardless of each other.

In this case:
A = Person does not have Covid
B = Test is negative

So we have:
P(A) = 0.95 (since 5% of the population has Covid, 95% does not),
P(B|A) = 0.999 (99.9% chance a person will test negative if they do not have Covid),
P(B) is the total probability of a negative test which can be found by adding the probability of a true negative to the probability of a false negative:

P(B) = P(B and A) + P(B and not A) = P(B|A)*P(A) + P(B|not A)*P(not A) = 0.999*0.95 + 0.35*0.05 = 0.94905 + 0.0175 = 0.96655

So we get:
P(A|B) = [P(B|A) * P(A)] / P(B) = (0.999 * 0.95) / 0.96655 = 0.981

So, the probability that the person does not have Covid given that they tested negative using this rapid test is roughly 98.1%.

Learn more about Bayes' Theorem here:

https://brainly.com/question/34293532

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