MP Board · Class 11 · Mathematics · ProbabilityIf $P(A) = 0.4$ and $P(A \cup B) = 0.7$, and $A, B$ are independent events, then $P(B)$ is:
Step-by-Step Solution
We know $P(A \cup B) = P(A) + P(B) - P(A \cap B)$. Since $A, B$ are independent, $P(A \cap B) = P(A)P(B)$. Thus, $0.7 = 0.4 + P(B) - 0.4P(B) \implies 0.3 = 0.6P(B) \implies P(B) = 0.5$.
Detailed Options Breakdown
Option : 0.3
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Probability.
Option 1: 0.4
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Probability.
Option 2: 0.5 (Correct Answer)
Correct choice. Refer to the step-by-step verified solution guidelines above for details.
Option 3: 0.6
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Probability.
💡 Study Guide: This question tests core syllabus concepts from Probability. For formulas, key summaries, and mock exam reference guides, read the full Probability Revision Notes.