Let \(D\) denote the event that you have the illness, and let \(S\) denote the event that the test signals positive. The probability requested can be denoted as \(P(D \mid S)\). The probability that the test correctly signals someone without the illness as negative is 0.95 . Consequently, the probability of a positive test without the illness is \[
P\left(S \mid D^{\prime}\right)=0.05 \]