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STD 11 - 14. probability — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 11 - 14. probability4 Marks
MCQ
For any two independent events ${E_1}$ and ${E_2},$ $P\,\{ ({E_1} \cup {E_2}) \cap ({\bar E_1} \cap {\bar E_2})\} $ is
  • ✓
    $ < \frac{1}{4}$
  • B
    $ > \frac{1}{4}$
  • C
    $ \ge \frac{1}{2}$
  • D
    None of these
✓

Answer

Correct option: A.
$ < \frac{1}{4}$
a
(a) Since $\overline {{E_1}} \cap \overline {{E_2}} = \overline {{E_1} \cup {E_2}} $ and $({E_1} \cup {E_2}) \cap (\overline {{E_1} \cup {E_2}} ) = \phi $

$P\,\{ ({E_1} \cup {E_2}) \cap (\overline {{E_1}} \cap \overline {{E_2}} )\} = P(\phi ) = 0 < \frac{1}{4}$.

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