Question:
If $P(A)=0.7, P(B)=0.5$ and $P(A\cup B)=0.9$, then $P(A/B)$ is ________.
If $P(A)=0.7, P(B)=0.5$ and $P(A\cup B)=0.9$, then $P(A/B)$ is ________.
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Always find the intersection first for conditional probability problems.
Updated On: Jun 26, 2026
- 0.3
- 0.4
- 0.5
- 0.6
- 0.7
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The Correct Option is D
Solution and Explanation
Step 1: Concept
Use the formula $P(A\cup B) = P(A) + P(B) - P(A\cap B)$.
Step 2: Meaning
$0.9 = 0.7 + 0.5 - P(A\cap B) \implies P(A\cap B) = 1.2 - 0.9 = 0.3$.
Step 3: Analysis
Conditional probability $P(A/B) = \frac{P(A\cap B)}{P(B)}$.
Step 4: Conclusion
$P(A/B) = 0.3 / 0.5 = 3/5 = 0.6$. Final Answer: (D)
Use the formula $P(A\cup B) = P(A) + P(B) - P(A\cap B)$.
Step 2: Meaning
$0.9 = 0.7 + 0.5 - P(A\cap B) \implies P(A\cap B) = 1.2 - 0.9 = 0.3$.
Step 3: Analysis
Conditional probability $P(A/B) = \frac{P(A\cap B)}{P(B)}$.
Step 4: Conclusion
$P(A/B) = 0.3 / 0.5 = 3/5 = 0.6$. Final Answer: (D)
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