WBJEE · Maths · Probability
For two events \(A\) and \(B,\) let \(P(A)=0.7\) and \(P(B)=0.6 .\) The necessarily false statement(s) is/are
- A \(P(A \cap B)=0.35\)
- B \(P(A \cap B)=0.45\)
- C \(P(A \cap B)=0.65\)
- D \(P(A \cap B)=0.28\)
Answer & Solution
Correct Answer
(D) \(P(A \cap B)=0.28\)
Step-by-step Solution
Detailed explanation
Given, \(P(A)=0.7\) and \(P(B)=0.6\) We know that \[ P(A \cap B) \leq P(B) \] \(\therefore \quad P(A \cap B) \leq 0.6\) From Booley's inequality \(P\left(\bigcap_{i=1}^{n} A_{i}\right) \geq \sum_{i=1}^{n} P\left(A_{i}\right)-(n-1)\)…
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