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

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

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

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



Answer :

GinnyAnswer
To determine the probability that the result of the test is positive given that the sample doesn't contain the bacteria, follow these steps:

1. Identify Relevant Data:
- The test results for samples that do not contain the bacteria:
- Test is positive: 58
- Test is negative: 1,872
- Total samples that do not contain the bacteria: 1,930

2. Set up the Probability Ratio:
- We are looking for the probability that the test is positive given that the sample does not contain the bacteria. This is calculated as:
[tex]\[ P(\text{Positive}|\text{No Bacteria}) = \frac{\text{Number of Positive Tests When No Bacteria is Present}}{\text{Total Samples that Do Not Contain Bacteria}} \][/tex]

3. Plug in the Values:
- Number of positive tests when no bacteria is present: [tex]\( 58 \)[/tex]
- Total samples that do not contain bacteria: [tex]\( 1,930 \)[/tex]

4. Calculate the Probability:
- Substitute the values into the formula:
[tex]\[ P(\text{Positive}|\text{No Bacteria}) = \frac{58}{1930} \][/tex]
- This ratio simplifies to approximately [tex]\(0.03005181347150259\)[/tex].

5. Select the Closest Answer:
- Among the given choices:
- A. 0.03
- B. 0.46
- C. 0.001
- D. 0.54
- The closest value to [tex]\(0.03005181347150259\)[/tex] is A. 0.03.

Therefore, the correct answer is:
A. 0.03

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