Let N be the total number of all securities.


Then 0.05N of them are "bad" securities.    ( (!) actually "bad", using the terminology from the condition).


The proposed system identifies 98% of these 0.05N "bad" securities as potentially bad;

    so, there are 0.98*0.05N potentially bad securities, from this pool.


The system also defines 15% of the rest, eligible securities as potentially bad. 

     So, there are addition 0.15*(1-0.05)N = 0.15*0.95N potentially bad securities, from the other pool.


In all, the number of potentially bad securities is the sum

     0.098*0.05N + 0.15*0.95N.


Now, the probability under the question is

    P =  =  =  = 0.339213.    ANSWER


It means that the "proposed system" recognizes actually bad securities among potentially bad securities with the probability about 0.34 only.

It is, actually, a  very low level recognition system.   ( It is enough to say, that it is WORST than tossing coin (!) )


At so low recognition level, it is better to vote AGAINST the system's predictions.


A good (or an ideal) system should recognize with the probability 0.9 - 0.95 - 0.98.