.
The events "pass an exam" and "fail to pass the exam" are COMPLEMENTARY events.
You either "pass an exam" or "fail to pass the exam", according to common sense of these words. *)
The sum of probabilities of these events is equal to 1.
Therefore, the probability of failing = 1 - probability of passing = 1 - 0.16 = 0.84. ANSWER
And it is true for any exam - not necessary consisting of 30 questions and not necessary consisting
of multiple choice questions.
The truth is
if the probability of passing an exam is 0.16, then the probability of failing the exam is the COMPLEMENT to it
and is equal to 1- 0.16 = 0.84.
The rest of the words in the post are placed intently to confuse the reader.
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*) In my solution above, I do not consider that case, for example, when answering, let say,
more than 20 arbitrary questions of 30 is declared as "passing", but answering, less or equal than 20 questions
is NOT necessary considered as failing.
Such situation is ALSO may happen in the life --- but it is a special case, which, as a special, should be specified by the rules.
In the area of common sense, the events "pass" and "fail to pass" are complementary, by default.
If the common sense is violated, than other rules should work --- and then they MUST BE declared in Math problem.
Otherwise, it is not a Math problem.
