Question:
Let \( A \) and \( B \) be two events. If \( P(A|B)=0.4 \), \( P(A|B')=0.7 \) and \( P(B)=0.7 \), then \( P(A) \) is
Let \( A \) and \( B \) be two events. If \( P(A|B)=0.4 \), \( P(A|B')=0.7 \) and \( P(B)=0.7 \), then \( P(A) \) is
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Always split probability using \(B\) and its complement.
Updated On: Apr 21, 2026
- \(0.44 \)
- \(0.54 \)
- \(0.49 \)
- \(0.5 \)
- \(0.65 \)
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The Correct Option is C
Solution and Explanation
Concept:
Total probability theorem:
\[
P(A) = P(A|B)P(B) + P(A|B')P(B')
\]
Step 1: Substitute values.
\[ P(B') = 1 - 0.7 = 0.3 \] \[ P(A) = 0.4 \cdot 0.7 + 0.7 \cdot 0.3 \]
Step 2: Compute.
\[ = 0.28 + 0.21 = 0.49 \]
Step 1: Substitute values.
\[ P(B') = 1 - 0.7 = 0.3 \] \[ P(A) = 0.4 \cdot 0.7 + 0.7 \cdot 0.3 \]
Step 2: Compute.
\[ = 0.28 + 0.21 = 0.49 \]
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