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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

  1. A \(P(A \cap B)=0.35\)
  2. B \(P(A \cap B)=0.45\)
  3. C \(P(A \cap B)=0.65\)
  4. D \(P(A \cap B)=0.28\)
Verified Solution

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 \(P\left(\bigcap_{i=1}^{n} A_{i}\right) \geq \sum_{i=1}^{n} P\left(A_{i}\right)-(n-1)\)…