Sorry, this must be laughably trivial, but I have to be sure. I am a grade 12 math tutor, and while running through some older exam questions I encountered this problem:
$$\text{If } P\left(N\right) = \frac{1}{4}\text{, determine } P\left(\overline{N}\right)$$
The multiple choice answers are:
$$\text{A. }\frac{-1}{4}\quad\text{B. }\frac{1}{4}\quad\text{C. }\frac{3}{4}\quad\text{D. }4$$
I eliminated A and D, because $0 \leq P(\text{Anything}) \leq 1$. My intuition tells me that $P\left(\overline{N}\right) = P\left(\lnot N\right)$ so the answer is C. Wolfram says that the bar could mean the arithmetic mean of a set of values or negation of a logical expression. Either way I would like some clarification on this notation.
Best Answer
In general, $\bar N$ means the complement of $N$ (i.e., everything except $N$).
So, $P(N)=1/4$ means that the probability of $N$ happening is $1/4$.
Therefore $P(\bar N)$ means the probability of everything except $N$, and this is $1-P(N) = 3/4$.