To find the probability of the union of two mutually exclusive events [tex]\(A\)[/tex] and [tex]\(B\)[/tex], we use the formula for the probability of the union of two events. Since [tex]\(A\)[/tex] and [tex]\(B\)[/tex] are mutually exclusive, this means they cannot happen at the same time, and their intersection is empty (i.e., [tex]\(P(A \cap B) = 0\)[/tex]).
The formula to find [tex]\(P(A \cup B)\)[/tex] (the probability that event [tex]\(A\)[/tex] or event [tex]\(B\)[/tex] occurs) is given by:
[tex]\[ P(A \cup B) = P(A) + P(B) \][/tex]
Given:
- [tex]\(P(A) = 0.60\)[/tex]
- [tex]\(P(B) = 0.20\)[/tex]
Now substitute the given probabilities into the formula:
[tex]\[ P(A \cup B) = 0.60 + 0.20 \][/tex]
Add the two probabilities together:
[tex]\[ P(A \cup B) = 0.80 \][/tex]
Therefore:
[tex]\[ P(A \text{ or } B) = 0.80 \][/tex]
The correct answer is [tex]\( \boxed{0.80} \)[/tex].
