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Probability — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsProbability1 Mark
MCQ
If $A$ and $B$ are two events and $A \neq \phi, B \neq \phi$, then
  • A
    $P(A \mid B)=P(A)\cdot P(B)$
  • ✓
    $P(A \mid B)=\frac{P(A \cap B)}{P(B)}$
  • C
    $P(A \mid B) \cdot P(B \mid A)=1$
  • D
    $P(A \mid B)=P(A) \mid P(B)$
✓

Answer

Correct option: B.
$P(A \mid B)=\frac{P(A \cap B)}{P(B)}$
(b) : By multiplication theorem,
$
\begin{aligned}
& P(A \cap B)=P(A \mid B) \times P(B)=P(B \mid A) \times P(A) \\
\Rightarrow & P(A \mid B)=\frac{P(A \cap B)}{P(B)}
\end{aligned}
$

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