Question

type the correct answer in the box. use numerals instead of words. if necessary, use / for the fraction bar.
the test to detect the presence of a certain protein is 98% accurate for corn plants that have the protein and 97% accurate for corn plants that do not have the protein.
do not round your answer.
if 3.6% of the corn plants in a given population actually have the protein, the probability that a randomly - chosen plant is detected incorrectly is

reset next

Explanation:

Step1: Calculate probability of incorrect detection for plants with protein

The test is 98% accurate for plants with the protein. So the probability of incorrect - detection for plants with the protein is $1 - 0.98=0.02$. The proportion of plants with the protein in the population is $0.038$. So the contribution to the overall incorrect - detection rate from plants with the protein is $0.038\times(1 - 0.98)=0.038\times0.02$.

Step2: Calculate probability of incorrect detection for plants without protein

The test is 97% accurate for plants without the protein. So the probability of incorrect - detection for plants without the protein is $1 - 0.97 = 0.03$. The proportion of plants without the protein in the population is $1 - 0.038=0.962$. So the contribution to the overall incorrect - detection rate from plants without the protein is $0.962\times(1 - 0.97)=0.962\times0.03$.

Step3: Calculate the total probability of incorrect detection

The total probability of incorrect detection $P$ is the sum of the two contributions above.
$P=0.038\times(1 - 0.98)+(1 - 0.038)\times(1 - 0.97)$
$P = 0.038\times0.02+0.962\times0.03$
$P=0.038\times0.02 + 0.962\times0.03=0.00076+0.02886$
$P = 0.02962$

Answer:

$0.02962$