Question

The test to detect the presence of respiratory syncytial virus is 97% accurate for a person who has the virus and 99% accurate for a person who does not have the virus. In a given population, 0.55% of the people are infected. The probability that a randomly chosen person gets an incorrect result is .

Answer 1

$\textrm{97 percent accurate for individual with the virus}$

$\text{3 percent inaccurate}$

$\textrm{99 percent accurate for an individual}$

$\textrm{1 percent inaccurate probability}$

$\textrm{Probability of infected:}$

$.0055$

$\textrm{Probability of not being infected}$

$1 - .0055 = .9945$

$\textrm{Combine it all together}$

$0.0055 * 0.03 + 0.9945 * 0.01 = 0.01011$

$\textrm{The probability that a randomly chosen person gets an incorrect result is 0.01011}$

$\textbf{Answer}$

$\textrm{0.01011}$