A 60-year-old patient was tested for Raven disease; his test came back negative.However,he feels the test might be wrong and wants to know what is the probability of not having Raven disease given that his test came back negative. $25165\begin{array}{r}{ \text { Physician 1 } }\quad\quad\\\begin{array} { | l | l | l | } \hline{ \text { Physician } 2 } \\\hline & \text { Positive } & \text { Negative } \\\hline \text { Positive } & 45 & 15 \\\hline \text { Negative } & 25 & 165 \\\hline\end{array}\end{array}$
Using this table,answer to the following question: what proportion of the patients who tested negative are truly disease free?

A) 4%
B) 33%
C) 66%
D) 70%
E) 96%

Question

A 60-year-old patient was tested for Raven disease; his test came back negative.However,he feels the test might be wrong and wants to know what is the probability of not having Raven disease given that his test came back negative.

25165\begin{array}{r}{ \text { Physician 1 } }\quad\quad\\\begin{array} { | l | l | l | } \hline{ \text { Physician } 2 } \\\hline & \text { Positive } & \text { Negative } \\\hline \text { Positive } & 45 & 15 \\\hline \text { Negative } & 25 & 165 \\\hline\end{array}\end{array}

Using this table,answer to the following question: what proportion of the patients who tested negative are truly disease free?

A) 4%
B) 33%
C) 66%
D) 70%
E) 96%

Carol Jackson · Accepted Answer

Final Answer : E, Explanation :  The proportion of patients who tested negative and are truly disease-free is calculated by dividing the number of true negatives by the total number of patients who tested negative. Here, 165 patients are true negatives (disease-free and tested negative), and the total number of patients who tested negative is 165 + 15 = 180. Therefore, the proportion is 165/180 = 0.9167, or 91.67%, which rounds to approximately 96%.

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