A pharmaceutical company develops a diagnostic test that can detect if an indivi

Question

A pharmaceutical company develops a diagnostic test that can detect if an individual has been infected with St¨upfenvirus. The test is positive 99.5% of the time if an individual has been infected with the virus. The test is positive 12% of the time even when the individual is not infected. For a certain population, the probability that a positively testing individual actually has been infected is 0.84681. Calculate the percentage of this population that has been infected with the St¨upfenvirus.

Explanation / Answer

let probability that a random person has been infected with the St¨upfenvirus =p

hence P(test postiive) =P(infected and test positive+not infected and test positive)

=p*0.995+(1-p)*0.12

threrefore probability of infected given tested positive =P(infected and test positive)/P(tested posiitve)

=p*0.995/(p*0.995+(1-p)*0.12) =0.84681

1.175p =0.995p+0.12-0.12p

0.3p=0.12

p=0.12/0.3 =0.4

therefore 40 percentage of this population that has been infected with the St¨upfenvirus

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