To find the probability of either event [tex]\( A \)[/tex] or event [tex]\( B \)[/tex] happening, denoted as [tex]\( P(A \cup B) \)[/tex], we use the fact that [tex]\( A \)[/tex] and [tex]\( B \)[/tex] are mutually exclusive events. This means that they cannot both occur at the same time, or in other words, the joint probability of [tex]\( A \)[/tex] and [tex]\( B \)[/tex] occurring together, [tex]\( P(A \cap B) \)[/tex], is zero.
The formula for the probability of the union of two events is:
[tex]\[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \][/tex]
Since [tex]\( A \)[/tex] and [tex]\( B \)[/tex] are mutually exclusive, [tex]\( P(A \cap B) = 0 \)[/tex]. Therefore, the formula simplifies to:
[tex]\[ P(A \cup B) = P(A) + P(B) \][/tex]
Given in the problem:
- [tex]\( P(A) = 0.60 \)[/tex]
- [tex]\( P(B) = 0.20 \)[/tex]
We substitute these values into the simplified formula:
[tex]\[ P(A \cup B) = 0.60 + 0.20 \][/tex]
[tex]\[ P(A \cup B) = 0.80 \][/tex]
Thus, the probability of either event [tex]\( A \)[/tex] or event [tex]\( B \)[/tex] happening is [tex]\( 0.80 \)[/tex].
So, the correct answer is [tex]\( \boxed{0.80} \)[/tex].
