If $P(A)=0.5, P(B)=0.4$, and $A$ and $B$ are mutually exclusive, find $P(A$ or $B)$. \[ P(A \text { or } B)=\Pi \text {. } \]

Step 1 ：Given that the events A and B are mutually exclusive, the probability of either event A or event B occurring is the sum of their individual probabilities.

Step 2 ：Let's denote the probability of event A as \(P(A)\) and the probability of event B as \(P(B)\).

Step 3 ：We are given that \(P(A) = 0.5\) and \(P(B) = 0.4\).

Step 4 ：Therefore, the probability of either event A or event B occurring, denoted as \(P(A \text{ or } B)\), is \(P(A) + P(B)\).

Step 5 ：Substituting the given values, we get \(P(A \text{ or } B) = 0.5 + 0.4 = 0.9\).

Step 6 ：Final Answer: The probability of either event A or event B occurring is \(\boxed{0.9}\).