Question

For two mutually exclusive events

• A. \(P(A \cup B) = P(A) + P(B)\)
• B. \(P(A \cup B) = P(A) \times P(B)\)
• C. \(P(A \cup B) = \frac{P(A) + P(B)}{P(A \cap B)}\)
• D. \(P(A \cup B) = P(A) - P(B)\)

Hint:

For mutually exclusive events, think of non-overlapping Venn diagrams.
Since they do not overlap, there is no shared region to subtract, so we simply add the probabilities.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Mutually exclusive events are events that cannot occur at the same time.
If event \(A\) occurs, event \(B\) cannot occur, meaning their intersection is an empty set.

Step 2: Key Formula or Approach:
The addition rule of probability for any two events \(A\) and \(B\) is:
\[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \] For mutually exclusive events, we have:
\[ A \cap B = \emptyset \implies P(A \cap B) = 0 \]

Step 3: Detailed Explanation:
By substituting the property of mutually exclusive events into the general addition rule:
\[ P(A \cup B) = P(A) + P(B) - 0 \] \[ P(A \cup B) = P(A) + P(B) \] Thus, the probability of the union of mutually exclusive events is simply the sum of their individual probabilities.

Step 4: Final Answer:
The correct option is 1, which corresponds to \(P(A \cup B) = P(A) + P(B)\).