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
doesn’t 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 doesn’t contain the bacteria?
a. 0.001
b. 0.03
c. 0.46
d. 0.54

Explanation:

Step1: Recall conditional - probability formula

The formula for conditional probability is $P(A|B)=\frac{P(A\cap B)}{P(B)}$. In the context of the table, if $A$ is the event that the test is positive and $B$ is the event that the sample doesn't contain bacteria, then $P(A|B)=\frac{\text{Number of positive - tests when no bacteria}}{\text{Total number of samples with no bacteria}}$.

Step2: Identify values from the table

The number of positive - tests when the sample doesn't contain bacteria is 58, and the total number of samples with no bacteria is 1930.

Step3: Calculate the probability

$P=\frac{58}{1930}\approx0.03$.

Answer:

B. 0.03