To determine the probability of either event [tex]\(A\)[/tex] or event [tex]\(B\)[/tex] occurring, given that [tex]\(A\)[/tex] and [tex]\(B\)[/tex] are mutually exclusive events, we use the formula for the probability of the union of two mutually exclusive events. This formula is:
[tex]\[ P(A \cup B) = P(A) + P(B) \][/tex]
Here, the probability of event [tex]\(A\)[/tex] is given as [tex]\(P(A) = 0.20\)[/tex], and the probability of event [tex]\(B\)[/tex] is given as [tex]\(P(B) = 0.40\)[/tex].
Since events [tex]\(A\)[/tex] and [tex]\(B\)[/tex] are mutually exclusive, it means they cannot happen at the same time. So, there is no overlap between the two events. Therefore, the probability of either [tex]\(A\)[/tex] or [tex]\(B\)[/tex] happening is simply the sum of their individual probabilities:
[tex]\[ P(A \cup B) = P(A) + P(B) \][/tex]
Substituting the given probabilities into the formula, we get:
[tex]\[ P(A \cup B) = 0.20 + 0.40 \][/tex]
Now, we sum the probabilities:
[tex]\[ P(A \cup B) = 0.60 \][/tex]
Therefore, the probability that either event [tex]\(A\)[/tex] or event [tex]\(B\)[/tex] occurs is [tex]\(0.60\)[/tex].
The correct answer is:
B. 0.60
