To determine the probability that the result of the test is positive given that the sample does not contain the bacteria, we can follow these steps:
1. Identify the relevant values from the table:
- The total number of samples that do not contain bacteria is 1,930.
- The number of samples that do not contain bacteria but test positive is 58.
2. Set up the probability formula:
- The probability that a test is positive given that the sample doesn't contain bacteria is calculated as:
[tex]\[
P(\text{Test is positive} \mid \text{No bacteria}) = \frac{\text{Number of positive tests with no bacteria}}{\text{Total number of samples with no bacteria}}
\][/tex]
3. Insert the values into the formula:
- Here, this translates to:
[tex]\[
P(\text{Test is positive} \mid \text{No bacteria}) = \frac{58}{1930}
\][/tex]
4. Calculate the probability:
- Performing this calculation gives the probability:
[tex]\[
\frac{58}{1930} \approx 0.03
\][/tex]
So, the probability that the result of the test is positive given that the sample doesn't contain the bacteria is approximately 0.03.
Considering the options provided:
A. 0.46
B. 0.001
C. 0.03
D. 0.54
The correct answer is:
C. 0.03
