Question

type the correct answer in the box. use numerals instead of words. the test to determine the presence of a certain virus in a pigeon is 97% accurate for a pigeon that has the virus and 99% accurate for a pigeon that does not have the virus. in a given population, 1.5% of the pigeons are infected. do not round your answer. the probability that a randomly selected pigeon gets an incorrect result is

Explanation:

Step1: Calculate probability of false - positive

The probability that a pigeon has the virus is $P(V)=0.015$, and the test is $97\%$ accurate for pigeons with the virus, so the probability of a false - negative for pigeons with the virus is $1 - 0.97=0.03$.
The probability that a pigeon does not have the virus is $P(
eg V)=1 - 0.015 = 0.985$, and the test is $99\%$ accurate for pigeons without the virus, so the probability of a false - positive for pigeons without the virus is $1 - 0.99 = 0.01$.

Step2: Use the law of total probability

The probability of an incorrect result $P(I)$ is the sum of the probability of a false - positive and the probability of a false - negative.
$P(I)=P(V)\times(1 - 0.97)+P(
eg V)\times(1 - 0.99)$
$P(I)=0.015\times0.03+0.985\times0.01$
$P(I)=0.015\times0.03 + 0.985\times0.01=0.00045+0.00985$
$P(I)=0.0103$

Answer:

$0.0103$