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Probability — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsProbability2 Marks
MCQ
$\begin{array}{l}\text { If } P ( B )=\frac{3}{4}, P (\overline{ A } \cap B \cap \overline{ C })=\frac{1}{3}, \\ P ( A \cap B \cap \overline{ C })=\frac{1}{3}, \text { then } P ( B \cap C )=\end{array}$
  • ✓
    $\frac{1}{12}$
  • B
    $\frac{3}{4}$
  • C
    $\frac{5}{12}$
  • D
    $\frac{23}{60}$
✓

Answer

Correct option: A.
$\frac{1}{12}$
(A)
$P ( B \cap C )= P ( B )-[ P ( A \cap B \cap \overline{ C })+ P (\overline{ A } \cap B \cap \overline{ C })]$
$=\frac{3}{4}-\frac{2}{3}=\frac{1}{12}$

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