Question

the accompanying table shows the results from a test for a certain disease. find the probability of selecting a subject with a negative test result, given that the subject has the disease. what would be an unfavorable consequence of this error? the individual actually had the disease: yes no positive 327 6 negative 18 1142

Explanation:

Step1: Recall conditional - probability formula

The formula for conditional probability is $P(A|B)=\frac{P(A\cap B)}{P(B)}$. In the context of a two - way table, if $A$ is the event of a negative test result and $B$ is the event of having the disease, then $P(A|B)=\frac{\text{Number of subjects with disease and negative test}}{\text{Number of subjects with disease}}$.

Step2: Identify relevant values from the table

The number of subjects with the disease is $327 + 18=345$ (sum of positive and negative test results for those with the disease). The number of subjects with the disease and a negative test result is $18$.

Step3: Calculate the probability

$P(\text{Negative}|\text{Disease})=\frac{18}{345}=\frac{6}{115}\approx0.052$

The unfavorable consequence of this error (false - negative) is that a person with the disease may not receive timely treatment, which can lead to the progression of the disease, increased risk of complications, and potentially worse health outcomes.

Answer:

The probability of selecting a subject with a negative test result, given that the subject has the disease, is $\frac{6}{115}\approx0.052$. The unfavorable consequence is delayed or lack of treatment leading to disease progression and complications.