To determine the probability of [tex]\( P(A \text{ or } B) \)[/tex], we can use the formula for the probability of the union of two events [tex]\( A \)[/tex] and [tex]\( B \)[/tex]:
[tex]\[ P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B) \][/tex]
This formula accounts for the fact that the events [tex]\( A \)[/tex] and [tex]\( B \)[/tex] may overlap, and thus without subtracting [tex]\( P(A \text{ and } B) \)[/tex], we would be counting the overlap twice.
Given the probabilities:
- [tex]\( P(A) = 0.60 \)[/tex]
- [tex]\( P(B) = 0.30 \)[/tex]
- [tex]\( P(A \text{ and } B) = 0.15 \)[/tex]
We substitute these values into the formula:
[tex]\[
P(A \text{ or } B) = 0.60 + 0.30 - 0.15
\][/tex]
First, add [tex]\( P(A) \)[/tex] and [tex]\( P(B) \)[/tex]:
[tex]\[
0.60 + 0.30 = 0.90
\][/tex]
Next, subtract [tex]\( P(A \text{ and } B) \)[/tex]:
[tex]\[
0.90 - 0.15 = 0.75
\][/tex]
Thus, the probability [tex]\( P(A \text{ or } B) \)[/tex] is:
[tex]\[
P(A \text{ or } B) = 0.75
\][/tex]
Therefore, the correct answer is:
[tex]\[
\boxed{0.75}
\][/tex]
This confirms that the probability of either event [tex]\( A \)[/tex] or event [tex]\( B \)[/tex] occurring is 0.75.
