Q:

Probability of answering correctly a question.

A student knows the 75% of the questions of the content (e.g. Biology). In the test, each question has four equally plausible answers when they don't know the correct answer.
Calculate the probability that the student answers correctly 1 question. 
This is what I did and I don't know whether it's correct:
$A$=Knowing the answer of a question of the content of biology, $P(A)=0.75$.
$B$=Answering correctly 1 question, $A\subset B$, 
$P(B)=P(A)+P(B\cap A^c)=P(A)+P(A^c)·P(B|A^c)=0.75+0.25·0.25=0.8125.$
I interpreted that $B|A^c$ is choosing the correct answer between the four options.
Everything is correct?

A:

Yes, everything is correct. To interpret this in the context of the question (without using set notation), 
$P(B)=P(\text{gets answer correct})\\=P(\text{{knows correct answer} or {{doesn't know correct answer} and {guesses correctly}}})\\=P(\text{knows correct answer})+P(\text{doesn't know correct answer})\cdot P(\text{guesses correctly})\\=0.75+0.25\cdot 0.25\\=0.8125$

