Refer to the table which summarizes the results of testing for a certain disease. $$\begin{array} { l | c c }
& \begin{array} { l }
\text { Positive } \
\text { Test Result }
\end{array} & \begin{array} { l }
\text { Negative } \
\text { Test Result }
\end{array} \
\hline \text { Subject has the disease } & 87 & 9 \
\text { Subject does not have the disease } & 27 & 312
\end{array}$$ A test subject is randomly selected and tested for the disease. What is the probability the subject has the disease given that the test result is negative?
A)0.094
B)0.028
C)0.972
D)0.221

Question

Refer to the table which summarizes the results of testing for a certain disease. $$\begin{array} { l | c c } 
& \begin{array} { l } 
\text { Positive } \
\text { Test Result }
\end{array} & \begin{array} { l } 
\text { Negative } \
\text { Test Result }
\end{array} \
\hline \text { Subject has the disease } & 87 & 9 \
\text { Subject does not have the disease } & 27 & 312
\end{array}$$ A test subject is randomly selected and tested for the disease. What is the probability the subject has the disease given that the test result is negative?
A)0.094
B)0.028
C)0.972
D)0.221

Quizplus · Accepted Answer

The probability that a subject has the disease given a negative test result is calculated using the formula P(A|B) = P(A and B) / P(B), where A is the event that the subject has the disease and B is the event of a negative test result. Here, P(A and B) = 9 (subjects who have the disease and tested negative) and P(B) = 9 + 312 (all subjects who tested negative). Thus, P(A|B) = 9 / (9 + 312) = 9 / 321 = 0.028.

Refer to the Table Which Summarizes the Results of Testing