In a normal distribution, are the events mutually exclusive or not, they are conditioned or not?

Question

I was solving some normal distribution exercises and the question appeared in the book:

$${\cal N}(10,2)$$

$$P(x < 8\ \vee\ x > 11)$$

So I thought, should I just sum or should subtract the intersection? And if I subtract the intersection, is it from conditioned events $(P (B.A) = P (A) .P (B / A))\ {\rm or\ not}\ (P (B.A) = P (A) .P (B)$?

Was that when I asked myself, in a normal distribution, are the events mutually exclusive or not, they are conditioned or not?

Answer 1

Does this figure help in this problem?