What is the probability of at least one person in a sample of k people being infected? Given the prevalence, sensitivity and specificity of a single test are known.

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.
