Question

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

	test is positive	test is negative	total
doesnt contain bacteria	58	1,872	1,930
total	126	1,874	2,000

what is the probability that the result of the test is positive, given that the sample doesnt contain the bacteria?
a. 0.03
b. 0.001
c. 0.46
d. 0.54

Explanation:

Step1: Identify relevant counts

We need the number of samples that don't contain bacteria and test positive (58) and the total number of samples that don't contain bacteria (1930).

Step2: Apply conditional probability formula

The formula for conditional probability \( P(A|B) = \frac{P(A \cap B)}{P(B)} \). In terms of counts, this is \( \frac{\text{Number of } B \text{ and } A}{\text{Number of } B} \). Here, \( A \) is "test positive" and \( B \) is "doesn't contain bacteria". So we calculate \( \frac{58}{1930} \).

Step3: Compute the value

\( \frac{58}{1930} \approx 0.03 \) (rounded to two decimal places).

Answer:

A. 0.03