Calculating Probabilities using a cumulative distribution function

Question

For (b)

Pr(X greater than or equal to 2) = ?

The textbook says as such but I am confused:

Pr(X greater than or equal to 2) = 1 - pr(X less than 2)

I do not understand why they re-write the probability, because doesn't Pr(X greater than or equal to 2) fit in the domain: x greater than 0? Why must we re-write this?

the answer then goes on to solve this

1 - F(2)

^ I dont understand why we can substitute 2 into F(x) only after re-writing the equation as 1- F(x) and not simply F(x)

Answer 1

We cannot substitute $2$ into $F(x)$ because $F(x)$ is by definition equal to $\Pr\{X\le x\}$ and we are looking for the probability $\Pr\{X\ge2\}$.

We have that $$ \Pr\{X\ge2\}=1-\Pr\{X<2\} $$ and $$ \Pr\{X<2\}=\Pr\{X\le2\} $$ since the random variable $X$ is continuous.

So the answer is $$ 1-F(2). $$