To determine the probability of the event [tex]\( A \)[/tex] or [tex]\( B \)[/tex] occurring, when [tex]\( A \)[/tex] and [tex]\( B \)[/tex] are mutually exclusive events, we use the addition rule for mutually exclusive events. The rule states:
[tex]\[ P(A \text{ or } B) = P(A) + P(B) \][/tex]
Since [tex]\( A \)[/tex] and [tex]\( B \)[/tex] are mutually exclusive, they cannot happen at the same time. Therefore, the probability of [tex]\( A \text{ or } B \)[/tex] is simply the sum of their individual probabilities.
Given:
[tex]\[ P(A) = 0.50 \][/tex]
[tex]\[ P(B) = 0.30 \][/tex]
Now, applying the rule:
[tex]\[ P(A \text{ or } B) = P(A) + P(B) \][/tex]
[tex]\[ P(A \text{ or } B) = 0.50 + 0.30 \][/tex]
[tex]\[ P(A \text{ or } B) = 0.80 \][/tex]
Hence, the probability of either event [tex]\( A \)[/tex] or event [tex]\( B \)[/tex] occurring is [tex]\( 0.80 \)[/tex].
The correct answer is:
D. 0.80
