Question

what is the probability of a positive test result from the metal detector given that a weapon is present? this is the sensitivity of the metal detector

Answer 1

We are asked to determine the probability of getting a positive result given that a weapon is present. This is equivalent to determining the probability of a true positive. To do that we will determine the quotient between the total number of true positive and the total number of times when there is a weapon, that is the sum of true positive and false negative, we get:

$P(+\parallel W)=\frac{102}{105}$

Solving the operations we get:

$P(+\parallel W)=0.9714$

Therefore, the probability is 0.9714 or in percentage form 97.14%.