NCERT · Class 11 · Mathematics · ProbabilityIf $A$ and $B$ are two events such that $P(A) = 0.5$, $P(B) = 0.3$ and $P(A \cap B) = 0.1$, then $P(A' \cap B')$ is equal to:
Step-by-Step Solution
By De Morgan's Law, $P(A' \cap B') = P((A \cup B)') = 1 - P(A \cup B)$. First, find $P(A \cup B) = P(A) + P(B) - P(A \cap B) = 0.5 + 0.3 - 0.1 = 0.7$. Then, $P(A' \cap B') = 1 - 0.7 = 0.3$.
Detailed Options Breakdown
Option : 0.3 (Correct Answer)
Correct choice. Refer to the step-by-step verified solution guidelines above for details.
Option 1: 0.2
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Probability.
Option 2: 0.5
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Probability.
Option 3: 0.9
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.