Question

Probability Puzzle 4: Disease Testing and False Positives

Assume that the test for some disease is 99% accurate. If somebody tests positive for that disease, is there a 99% chance that thet have the disease?

Answer 1

Let us first define the terms.

True Positive, TP = Disease is actually present and it test positive as well

True Negative, TN = Disease is not actually present and it test negative as well

False Positive, FP = Disease is not actually present but it tests positive

False Negative, FN = Disease is actually present but it tests negative

Accuracy = Number of correct assessments/Number of all assessments

= (TP + TN)/(TP + TN + FP + FN)

-> TP + TN = 0.99(TP + TN + FP + FN)

Now, Sensitivity = TP/(TP + FN) = Number of true positive assessments/Number of all positive assessment

Thus, it cannot be inferred that there is a 99% chance that they have the disease given that somebody tests positive for that disease.