To determine the probability that the result of the test is positive, given that the sample doesn't contain the bacteria, we need to focus on the relevant data.
First, let's observe the total number of samples that don't contain bacteria:
[tex]\[
\text{Samples that don't contain bacteria} = 1,930
\][/tex]
Next, we identify how many of these samples tested positive, despite not containing bacteria. These are our false positives:
[tex]\[
\text{False positives} = 58
\][/tex]
The probability we are looking for is the fraction of false positives out of the total number of samples that don't contain the bacteria. This is calculated as follows:
[tex]\[
\text{Probability} = \frac{\text{False positives}}{\text{Samples that don't contain bacteria}} = \frac{58}{1,930}
\][/tex]
From this calculation, the probability is:
[tex]\[
0.03005181347150259
\][/tex]
This value rounds to 0.03.
Therefore, the correct answer is:
A. 0.03
