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AP EAMCET · Maths · Probability

\(E_1\) and \(E_2\) are two independent events of a random experiment such that \(P\left(E_1\right)=\frac{1}{2}\) and \(P\left(E_1 \cup E_2\right)=\frac{2}{3}\).
Then match the items of List-I with the items of List-II.

The correct match is

  1. A A-iii; B-iv; \(\quad\) C-i; \(\quad\) D-v
  2. B A-iii; B-i; \(\quad\) C-v; \(\quad\) D-ii
  3. C A-i; \(\quad\) B-v; \(\quad\) C-ii; \(\quad\) D-iv
  4. D A-v; \(\quad\) B-i; \(\quad\) C-iii; \(\quad\) D-ii
Verified Solution

Answer & Solution

Correct Answer

(B) A-iii; B-i; \(\quad\) C-v; \(\quad\) D-ii

Step-by-step Solution

Detailed explanation

\(\mathrm{P}\left(\mathrm{E}_1\right)=\frac{1}{2}, \mathrm{P}\left(\mathrm{E}_1 \cup \mathrm{E}_2\right)=\frac{2}{3}\) Since, \(E_1\) and \(E_2\) are independent events \(\therefore P\left(E_1 \cap E_2\right)=P\left(E_1\right) P\left(E_2\right)\)…