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Part of 2018 Iran MO (1st Round)

Problems(1)

COVID-related probability problem - Iran First Round 2018, P1

Source:

3/6/2021
In a village with a population of 10001000, two hundred people have been infected by a disease. A diagnostic test can be done to check whether a person is infected, but the result could be erroneous. That is, there is a 5%5\% probability that the test result of an infected person shows that they are not infected and a 5%5\% probability that the test result of a healthy person shows that they are infected. We randomly choose someone from the population of this village and take the diagnostic test from him. What is the probability that the test result declares that person is infected?
probabilitypercent