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TS EAMCET · Maths · Probability

\(E_1\) and \(E_2\) are two independent events of a random experiment with \(P\left(E_1\right)=\frac{1}{2}\) and \(P\left(E_1 \cup E_2\right)=\frac{2}{3}\). Then match the items of List-1 with those of List-II.
The correct match is \(\begin{array}{lllllllll}A & \text { B } & \text { C } & \text { D } & \text { A } & \text { B } & \text { C } & \text { D }\end{array}\)

  1. A \(\begin{array}{llll}\text { III } & \text { II } & \text { I } & \text { IV }\end{array}\)
  2. B III IV I II
  3. C \(\begin{array}{llll} & \text { III } & \text { II } & \text { I }\end{array}\)
  4. D \(\begin{array}{llll}\text { IV } & \text { III } & \text { I } & \text { II }\end{array}\)
Verified Solution

Answer & Solution

Correct Answer

(B) III IV I II

Step-by-step Solution

Detailed explanation

We have, \(P\left(E_1\right)=\frac{1}{2}\) and \(P\left(E_1 \cup E_2\right)=\frac{2}{3}\). Since, \(E_1\) and \(E_2\) are independent events \(\therefore \quad P\left(E_1 \cap E_2\right)=P\left(E_1\right) \times P\left(E_2\right)\) Let \(P\left(E_2\right)\) be \(x\). Then,…