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

Let $[x]$ denote the integral part of $x \in R.$ $g(x) = x - [x]$. Let $f(x)$ be any continuous function with $f(0) = f(1)$ then the function $h(x) = f(g(x))$ :
→
The area of the region enclosed between the parabolas $y ^{2}=2 x -1$ and $y ^{2}=4 x -3$ is
→
If the system of linear equations $x + y + z = 5$ ; $x = 2y + 2z = 6$ ; $x + 3y + \lambda z = u (\lambda \, \mu \in R)$, has infinitely many solutions then the value of $\lambda  + \mu $ is
→
For any three vectors $\vec{\text{a}},\vec{\text{b}},\vec{\text{c}}$ the expression $\big(\vec{\text{a}}-\vec{\text{b}}\big).\big\{\big(\vec{\text{b}}-\vec{\text{c}}\big)\times\big(\vec{\text{c}}-\vec{\text{a}}\big)\big\}$ equals:
→
If $A$ is a skew symmetric matrix, then $∣A∣$ is
→
Let $\begin{vmatrix}\text{x}^2+3\text{x}&\text{x}-1&\text{x}+ 3\\\text{x}+1&-2\text{x}&\text{x}-4\\\text{x}-3&\text{x}+4&3\text{x}\end{vmatrix}=\text{ax}^4+\text{bx}^3+\text{cx}^2+\text{dx}+\text{e}$ be an identity in $x,$ where $a, b, c, d, e$ are independent of $x.$ Then the value of $e$ is:
→
If ${l_1},\,{m_1},\,{n_1}$ and ${l_2},{m_2},{n_2}$ are the direction cosines of two perpendicular lines, then the direction cosine of the line which is perpendicular to both the lines, will be
→
Let a function $f: N \rightarrow N$ be defined by

$f ( n )=\left[\begin{array}{ll}2 n , \,\,\, \,\,\,\,\,\,n =2,4,6,8, \ldots . \\ n -1,\,\,\,  n =3,7,11,15, \ldots . \\ \frac{ n +1}{2}, \,\,\, \,\,\,n =1,5,9,13, \ldots \ldots\end{array}\right.$

then, $f$ is

→
Order of $\left[ {x\,y\,z} \right]\,\left[ {\begin{array}{*{20}{c}}
a&h&g\\
h&b&f\\
g&f&c
\end{array}} \right]\,\left[ {\begin{array}{*{20}{c}}
x\\
y\\
z
\end{array}} \right]$ is
→
If the value of the integral $\int\limits_1^2 {\,{e^{{x^2}}}} dx$ is $\alpha$ , then the value of $\int\limits_e^{{e^4}} {\,\,\sqrt {\ell n\,x} }\, dx$ is :
→