2.
In this question you must show detailed reasoning.
A disease that affects trees shows no visible evidence for the first few years after the tree is infected.
A test has been developed to determine whether a particular tree has the disease. A positive result to the test suggests that the tree has the disease. However, the test is not \(100 \%\) reliable, and a researcher uses the following model.
- If the tree has the disease, the probability of a positive result is 0.95 .
- If the tree does not have the disease, the probability of a positive result is 0.1 .
- It is known that in a certain county, \(A , 35 \%\) of the trees have the disease. A tree in county \(A\) is chosen at random and is tested.
Given that the result is positive, determine the probability that this tree has the disease.
A forestry company wants to determine what proportion of trees in another county, \(B\), have the disease. They choose a large random sample of trees in county \(B\).
Each tree in the sample is tested and it is found that the result is positive for \(43 \%\) of these trees.
By carrying out a calculation, determine an estimate of the proportion of trees in county \(B\) that have the disease.
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