Answer:
0.1322 = 13.22% probability that the soldier is mal-adjusted.
Explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is

In which
P(B|A) is the probability of event B happening, given that A happened.
is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Positive test
Event B: Soldier is mal-adjusted.
Probability of a positive test:
55% of 5%(mal-adjusted).
19% of 100 - 5 = 95%(well adjusted). So

Probability of a positive test and soldier being mal-adjusted.
55% of 5%. So

What is the probability that the soldier is mal-adjusted?

0.1322 = 13.22% probability that the soldier is mal-adjusted.