Question

A certain disease has an incidence rate of 0.6%. If the false negative rate is 4% and the false positive rate is 4%, computethe probability that a person who tests positive actually has the disease.Give your answer accurate to at least 3 decimal places. (13 decimal places)

Answer 1

Given:

A certain disease has an incidence rate 0.6%. If the false negative rate is 4% and the false positive rate is 4%.

To know:

Probability that a person who tests positive actually has the disease.

Explanation:

We can use Bayes theorem to calculate.

Solution:

$\begin{gathered} P\left(disease\left|positive\right?\right)=\frac{\left(0.006\right)\left(0.96\right)}{\left(0.006\right)\left(0.96\right)+\left(0.994\right)\left(0.04\right)} \\ \approx0.126 \end{gathered}$

Hence 0.126 is the required probability.