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A firm has developed a new test for COVID-19. If someone has COVID-19, the test finds...

A firm has developed a new test for COVID-19. If someone has COVID-19, the test finds it 93% of the time. If someone does not have COVID-19 the test returns positive for COVID-19 8% of the time. If the 30% of the populations has COVID-19, what is the probability of someone selected at random having COVID-19 if they tested positive? Give your answer to four decimal places

math   Statistics-And-Probability   
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Answer #1

P(has COVID-19) = 0.3

P(tests positive | has COVID-19) = 0.93

P(tests positive | doesn't have COVID-19) = 0.08

P(tests positive) = P(tests positive | has COVID-19) * P(has COVID-19) + P(tests positive | doesn't have COVID-19) * P(doesn't have COVID-19)

                          = 0.93 * 0.3 + 0.08 * (1 - 0.3)

                          = 0.335

P(has COVID-19 | tested positive) = P(tests positive | has COVID-19) * P(has COVID-19) / P(tests positive)

                                                       = 0.93 * 0.3 / 0.335

                                                       = 0.8328

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