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Question: to ascertain the effectiveness of a new quicker and simpler...

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To ascertain the effectiveness of a new, quicker, and simpler test for identifying COVID-19, a study was undertaken involving 914 participants. With this test, a positive result indicates the presence of COVID-19. A negative result indicates the absence of COVID-19. Data collected to assess the effectiveness of this new test revealed:

  • 221 of the participants confirmed they actually had COVID-19, with the other participants confirming they actually did not have COVID-19.
  • 172 participants actually had COVID-19 and produced a negative test result.
  • 294 participants produced a negative test result.

A participant from the study is chosen at random. What is the probability they do actually have COVID-19 given the test result is positive? (3 decimal places)

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