Question

select the correct answer.
arborists use a test to detect the presence of a certain pathogen in fruit trees. the test gives a positive result 96% of the time if a tree has a disease, and it is 97% accurate for trees that do not have the disease.
given that a tree does not have the pathogen it is being tested for, what is the probability of getting a positive result?
a. 0.01
b. 0.03
c. 0.07
d. 0.04

Explanation:

Step1: Understand the problem

We need to find the probability of a positive test result given that the tree does not have the pathogen. The test is 97% accurate for trees without the disease, so the false positive rate (probability of positive when not diseased) is \(1 - 0.97\).

Step2: Calculate the false positive rate

The accuracy for non - diseased trees is 97% or 0.97. The probability of a positive result when the tree is not diseased (false positive) is \(1 - 0.97=0.03\).

Answer:

B. 0.03