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The results from a test to detect the presence of bacteria in a sample are shown in the table.

[tex]\[
\begin{tabular}{|l|c|c|c|}
\hline & \text{Test is positive} & \text{Test is negative} & \text{Total} \\
\hline \text{Contains bacteria} & 68 & 2 & 70 \\
\hline \begin{tabular}{l}
\text{Doesn't contain} \\
\text{bacteria}
\end{tabular} & 58 & 1,872 & 1,930 \\
\hline \text{Total} & 126 & 1,874 & 2,000 \\
\hline
\end{tabular}
\][/tex]

What is the probability that the result of the test is positive, given that the sample doesn't contain the bacteria?

A. 0.46
B. 0.001
C. 0.03
D. 0.54



Answer :

GinnyAnswer
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

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