Chapter 8, Problem 1CE

To determine

To calculate: Probability of test to be positive when there is no disease $P\left(T|D^{\prime }\right)$.

Answer to Problem 1CE

Solution:

Probability of test to be positive when there is no disease is $\underset{\_}{0.001}$.

Explanation of Solution

Given:

Specificity of the test is $0.999$.

Formula used:

$P\left(T|D^{\prime }\right)=1-P\left(T^{\prime }|D^{\prime }\right)$

Calculation:

The probability of patient not having disease also the test gives a negative result is called specificity of the test, represented by $P\left(T^{\prime }|D^{\prime }\right)$.

While on the other hand, $P\left(T|D^{\prime }\right)$, represents the probability of test to be positive even though there is no disease.

Also, the relation between them is given by:

$P\left(T|D^{\prime }\right)=1-P\left(T^{\prime }|D^{\prime }\right)$

Therefore, substitute value of $P\left(T^{\prime }|D^{\prime }\right)$ to calculate specificity:

$\begin{array}{c}P\left(T|D^{\prime }\right)=1-P\left(T^{\prime }|D^{\prime }\right)\\ =1-0.999\\ =0.001\end{array}$

Hence, the probability of test to be positive when there is no disease is $0.001$.