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Given the prevalence, sensitivity and specificity of a single test are known.

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You only need one of the three measures

  • prevalence the proportion of the population that has a certain condition

  • sensitivity the probability that a unit that is truly positive will test positive.

    In simple words: 'how well does the test detect positive cases'

  • specificity the probability that a unit that is truly negative will test negative.

    In simple words: 'how well does the test ignore negative cases'.

Your question relates to the probability that a people are infected (in a sample of size 'k'). Which quantity do you need to compute this? Hint: the sensitivity and specificity relate to the situation when there has been a test, your question does not mention anything about test results.

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