Question
Download Solution PDFIf A and B are mutually exclusive events and P(A∪B) ≠ 0 then P(A/A ∪ B) equals to :
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
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) \(\frac{P(A)}{P(A) + P(B)}\).
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