what is the probability of a positive test result from the metal detector ?

To get the probability of a positive test, we need to add the true positives to the false positives and divide the result by the total number of tests, as shown below
[tex]P(positive)=\frac{102+188}{365}=\frac{290}{365}=\frac{58}{73}=0.79452054\ldots[/tex]Finally, rounding the answer,
[tex]\Rightarrow P(positive)\approx0.79[/tex]The answer is 0.79