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 the probability is 0.052 (round to three decimal places as needed.) what would be an unfavorable consequence of this error? a. the test would be shown to be not effective. b. the subject would experience needless stress and additional testing. c. the subject would not receive treatment and could spread the disease. d. the test would be shown to be not reliable.

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 this problem, let $A$ be the event of a negative test result and $B$ be 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 values from the table

The number of subjects with the disease and a negative - test result is 18, and the number of subjects with the disease is $327 + 18=345$.

Step3: Calculate the probability

$P(A|B)=\frac{18}{345}\approx0.052$ (rounded to three decimal places).

For the second part, if a subject has the disease but gets a negative test result:

• A subject who has the disease but is misclassified as negative will not receive treatment. Also, since they are unaware of their condition, they could potentially spread the disease to others.

Answer:

The probability is 0.052.
C. The subject would not receive treatment and could spread the disease.