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Probability — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsProbability2 Marks
MCQ
For any two independent events $E _1$ and $E _2$, $P \left\{\left( E _1 \cup E _2\right) \cap\left(\overline{ E }_1 \cap \overline{ E }_2\right)\right\}$ is
  • ✓
    $<\frac{1}{4}$
  • B
    $>\frac{1}{4}$
  • C
    $\geq \frac{1}{2}$
  • D
    None of these
✓

Answer

Correct option: A.
$<\frac{1}{4}$
(A)
Since $\overline{ E _1} \cap \overline{ E _2}=\overline{ E _1 \cup E _2}$
and $\left( E _1 \cup E _2\right) \cap\left(\overline{ E _1 \cup E _2}\right)=\phi$
$\therefore \quad P \left\{\left( E _1 \cup E _2\right) \cap\left( E _1 \cap E _2\right)\right\}= P (\phi)=0<\frac{1}{4}$

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