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TS EAMCET · Maths · Probability

Two events \(A\) and \(B\) are such that \(P(A)=\frac{1}{4}, P(A / B)=\frac{1}{4}\) and \(P(B / A)=\frac{1}{2}\). Consider the following statements : (I) \(P(\bar{A} / \bar{B})=\frac{3}{4}\) (II) \(A\) and \(B\) are mutually exclusive (III) \(P(A / B)+P(A / \bar{B})=1\) Then,

  1. A only (l) is correct
  2. B only (I) and (II) are correct
  3. C only (I) and (III) are correct
  4. D only (II) and (III) are correct
Verified Solution

Answer & Solution

Correct Answer

(A) only (l) is correct

Step-by-step Solution

Detailed explanation

We have, \(P(A)=\frac{1}{4}, P\left(\frac{A}{B}\right)=\frac{1}{4}\) and \(P\left(\frac{B}{A}\right)=\frac{1}{2}\) Now, \(\quad P\left(\frac{A}{B}\right)=\frac{P(A \cap B)}{P(B)}=\frac{1}{4}\) and \(\quad P\left(\frac{B}{A}\right)=\frac{P(A \cap B)}{P(A)}=\frac{1}{2}\)…