If A and B are mutually exclusive events and P(A∪B) ≠ 0 then P(A/A ∪ B) equals to :

Concept:

For mutually exclusive events A and B, the conditional probability  \(P(A | A \cup B)\)  represents the probability of A occurring given that either A or B has occurred.

Calculation:

Given:

A and B are mutually exclusive events \(( P(A \cap B) = 0)\)
\( P(A \cup B) \neq 0 \)

Solution:

1. The conditional probability formula:
\( P(A | A \cup B) = \frac{P(A \cap (A \cup B))}{P(A \cup B)} \)

2. For mutually exclusive events:
\( P(A \cap (A \cup B)) = P(A) \)
\( P(A \cup B) = P(A) + P(B) \)

3. Therefore:
\( P(A | A \cup B) = \frac{P(A)}{P(A) + P(B)} \)

Final Answer:

The correct expression is 1) \(\frac{P(A)}{P(A) + P(B)}\).