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

CBSE BoardEnglish MediumSTD 11 ScienceMathsSTD 11 - 14. probability1 Mark
MCQ
For three non impossible events $A$, $B$ and $C$ $P\left( {A \cap B \cap C} \right) = 0,P\left( {A \cup B \cup C} \right) = \frac{3}{4},$ $P\left( {A \cap B} \right) = \frac{1}{3}$ and $P\left( C \right) = \frac{1}{6}$.

The probability, exactly one of $A$ or $B$ occurs but $C$ doesn't occur is 

  • A
    $\frac{1}{{12}}$
  • B
    $\frac{5}{{6}}$
  • ✓
    $\frac{1}{{4}}$
  • D
    $\frac{2}{{3}}$
✓

Answer

Correct option: C.
$\frac{1}{{4}}$
c
$\mathrm{P}([(\mathrm{A} \cap \overline{\mathrm{B}}) \cup(\overline{\mathrm{A}} \cap \mathrm{B})] \cap \overline{\mathrm{C}})$

$=\frac{3}{4}-\left\{\frac{1}{3}+\frac{1}{6}\right\}=\frac{1}{4}$

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