Question

In a cross-sectional study conducted at a clinic, the researcher is interested to know what proportion of the patients is suffering from tuberculosis and HIV.

\[ \begin{array}{|c|c|c|} \hline & \text{Tuberculosis (Yes)} & \text{Tuberculosis (No)} \\ \hline \text{HIV +ve} & 16 & 4 \\ \hline \text{HIV -ve} & 24 & 456 \\ \hline \end{array} \]

The probability that a person selected is not suffering from both tuberculosis and HIV is:

• A. 0.8
• B. 0.2
• C. 0.912
• D. 0.962

Hint:

Use complement rule: \[ P(\text{Not }A)=1-P(A) \]

Answer 1

The Correct Option is D

Step 1: Find total number of patients.
\[ 16+4+24+456 = 500 \]

Step 2: Find patients suffering from both HIV and Tuberculosis.
\[ 16 \]

Step 3: Find probability of suffering from both diseases.
\[ P(\text{Both}) = \frac{16}{500} = 0.032 \]

Step 4: Find probability of not suffering from both diseases.
\[ 1-0.032 = 0.968 \]

Step 5: Choose nearest option.
The exact answer is \[ {0.968} \] The paper appears to contain a printing error. The nearest listed option is \[ {0.962} \] Hence expected answer: \[ {\text{Option (D)}} \]