To understand the probability of the intersection of [tex]\(A\)[/tex] and [tex]\(B\)[/tex], we need to use the given information about the properties of these events and their individual probabilities.
Mutually exclusive events are events that cannot occur at the same time. In other words, if [tex]\(A\)[/tex] and [tex]\(B\)[/tex] are mutually exclusive, the probability that both [tex]\(A\)[/tex] and [tex]\(B\)[/tex] occur together is zero.
We are given that:
- Event [tex]\(A\)[/tex] and Event [tex]\(B\)[/tex] are mutually exclusive.
- [tex]\(P(A) = 0.45\)[/tex]
- [tex]\(P(B) = 0.35\)[/tex]
Since [tex]\(A\)[/tex] and [tex]\(B\)[/tex] are mutually exclusive, the probability of the intersection of [tex]\(A\)[/tex] and [tex]\(B\)[/tex] is [tex]\(0\)[/tex].
Therefore,
[tex]\[ P(A \cap B) = 0 \][/tex]
So the answer to the question is:
[tex]\[ \boxed{0} \][/tex]
