Question:
A and B are mutually exclusive events of a random experiment and \( P(B^c) \ne 1 \), then
\[
P(A | B^c) = ?
\]
A and B are mutually exclusive events of a random experiment and \( P(B^c) \ne 1 \), then
\[
P(A | B^c) = ?
\]
Show Hint
Mutually exclusive means no overlap — use this to simplify intersections in conditional probability.
Updated On: May 13, 2025
- \( \frac{P(A)}{1 - P(B)} \)
- \( \frac{P(B)}{1 - P(A)} \)
- \( \frac{P(A)}{1 + P(B)} \)
- \( \frac{P(A)}{P(A) + P(B)} \)
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The Correct Option is A
Solution and Explanation
Since A and B are mutually exclusive: \( A \cap B = \emptyset \Rightarrow A \subseteq B^c \)
Using definition of conditional probability:
\[
P(A | B^c) = \frac{P(A \cap B^c)}{P(B^c)} = \frac{P(A)}{1 - P(B)}
\]
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