Download App

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}
$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from Probability→Probability — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

If the equation ${\sin ^{ - 1}}\sqrt x  + {\cos ^{ - 1}}\sqrt {{x^2} - 1}  + {\tan ^{ - 1}}\left( {\tan \,y} \right) = a$ has at least one solution, then number of integral values of $a$ is 
→
If the shortest distance between the lines $\frac{x-4}{1}=\frac{y+1}{2}=\frac{z}{-3}$ and $\frac{x-\lambda}{2}=\frac{y+1}{4}=\frac{z-2}{-5}$ is $\frac{6}{\sqrt{5}}$, then the sum of all possible values of $\lambda$ is :
→
Consider $f(x)=\left\{\begin{matrix}
tan^{-1}(\frac{\alpha x+\beta}{\gamma})\ \ \ x\in(0,\frac{1}{2}) and   \\0  \ \ \  \ \ \ \ x=\frac{1}{2}
 and \\ ln(\beta x^2 +2) \ \ \ \ \ \ x\in(\frac{1}{2},1) 
and\end{matrix}\right.$  . If $f(x)$ continuous and derivable in its domain then the value of $\alpha + \beta + \gamma$ is-
→
Let the tangent at any point $P$ on a curve passing through the points $(1,1)$ and $\left(\frac{1}{10}, 100\right)$, intersect positive $x$-axis and $y$-axis at the points $A$ and $B$ respectively. If $P A: P B=1: k$ and $y=y(x)$ is the solution of the differential equation $e^{\frac{d y}{d x}}=k x+\frac{k}{2}$, $y(0)=k$, then $4 y(1)-5 \log _e 3$ is equal to $.........$.
→
${\sin ^{ - 1}}\frac{{\sqrt x }}{{\sqrt {x + a} }}$ is equal to
→
Let $f:[-1,1] \rightarrow R$ be defined as $f(x)=a x^{2}+b x+c$ for all $x \in[-1,1],$ where $a , b , c \in R$ such that $f (-1)=2, f ^{\prime}(-1)=1$ and for $x \in(-1,1)$ the maximum value of $f ^{\prime \prime}( x )$ is $\frac{1}{2} .$ If $f ( x ) \leq \alpha$ , $x \in[-1,1],$ then the least value of $\alpha$ is equal to ...... .
→
If a line makes angle $\alpha,\beta$ and $\gamma$ with the axes respectively, then $\cos2\alpha+\cos2\beta+\cos2\gamma=$
  1. -2
  2. -1
  3. 1
  4. 2
→
If $\left( {\frac{{2 + \sin x}}{{1 + y}}} \right)\frac{{dy}}{{dx}} = - \cos x,\;y(0) = 1,$ then $y{\rm{ }}\left( {\frac{\pi }{2}} \right)$=
→
For a steamer the consumption of petrol (per hour) varies as the cube of its speed (in km). If the speed of the current is steady at $C \,\,km/hr$ then the most economical speed of the steamer going against the current will be ........... $C$.
→
Let $\text{f(x)}=|\cos\text{x}|.$ Then,
  1. f(x) is everywhere differentiable.
  2. f(x) is everywhere continuous but not differentiable at $\text{x}=\text{n}\pi,\text{n}\in\text{Z}$
  3. f(x) is everywhere continuous but not differentiable at $\text{x}=(2\text{n}+1)\frac{\pi}{2},\text{n}\in\text{Z}.$
  4. None of these.
→