Download App

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

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 11 - 14. probability4 Marks
MCQ
From eighty cards numbered $1$ to $80$, two cards are selected randomly. The probability that both the cards have the numbers divisible by $4$ is given by
  • A
    $\frac{{21}}{{316}}$
  • ✓
    $\frac{{19}}{{316}}$
  • C
    $\frac{1}{4}$
  • D
    None of these
✓

Answer

Correct option: B.
$\frac{{19}}{{316}}$
b
(b) Total number of ways $ = {\,^{80}}{C_2}$

and favorable ways ${ = ^{20}}{C_2}$

$\therefore$ Required probability $P = \frac{{^{20}{C_{_2}}}}{{^{80}{C_2}}} = \frac{{19}}{{316}}$.

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

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

$\int_1^2 {\frac{{\cos (\log x)}}{x}} \,dx = $
→
Let $n \geq 3$. A list of numbers $x_1, x, \ldots, x_n$ has mean $\mu$ and standard deviation $\sigma$. A new list of numbers $y_1, y_2, \ldots, y_n$ is made as follows $y_1=\frac{x_1+x_2}{2}, y_2=\frac{x_1+x_2}{2}$ and $y_j=x_j$ for $j=3,4, \ldots, n$.

The mean and the standard deviation of the new list are $\hat{\mu}$ and $\hat{\sigma}$. Then, which of the following is necessarily true?

→
If matrix $A = \left[ {\begin{array}{*{20}{c}}0&{ - 1}\\1&0\end{array}} \right]$, then ${A^{16}} = $
→
If in a $G.P$. of $64 $ terms, the sum of all the terms is $7$ times the sum of the odd terms of the $G.P,$ then the common ratio of the $G.P$. is equal to
→
Let $\vec{a}, \vec{b}$ and $\vec{c}$ be three units vectors such that $\overrightarrow{\mathrm{a}}+\overrightarrow{\mathrm{b}}+\overrightarrow{\mathrm{c}}=\overrightarrow{0} .$ If $\lambda=\overrightarrow{\mathrm{a}} \cdot \overrightarrow{\mathrm{b}}+\overrightarrow{\mathrm{b}} \cdot \overrightarrow{\mathrm{c}}+\overrightarrow{\mathrm{c}} \cdot \overrightarrow{\mathrm{a}} $ and $\overrightarrow{\mathrm{d}}=\overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{b}}+\overrightarrow{\mathrm{b}} \times \overrightarrow{\mathrm{c}}+\overrightarrow{\mathrm{c}} \times \overrightarrow{\mathrm{a}},$ then the ordered pair $(\lambda, {\mathrm{\vec d}})$ is equal to 
→
The equation of the hyperbola whose foci are $(-2, 0)$ and $(2, 0)$ and eccentricity is $2$ is given by :-
→
Let $\int {{{\sec }^{ - 1}}\left[ {{{- \sin }^2}x} \right]dx}  = f\left( x \right) + C$ , (valid $x  \ne 0$ ) where $[k]$ denotes greatest integer less than or equal to $k$ and $f(0) = 0$ , then the value of ${\left( {f\left( {\frac{8}{{\pi x}}} \right)} \right)"}$ at $x = 2$ is (where $(')$ dash denotes the derivative)
→
Consider the lines $x(3 \lambda+1)+y(7 \lambda+2)=17 \lambda+5$, $\lambda$ being a parameter, all passing through a point P . One of these lines (say L) is farthest from the origin. If the distance of $L$ from the point $(3,6)$ is $d$, then the value of $d^{2}$ is
→
Let $\mathrm{ABC}$ be an equilateral triangle. A new triangle is formed by joining the middle points of all sides of the triangle $\mathrm{ABC}$ and the same process is repeated infinitely many times. If $\mathrm{P}$ is the sum of perimeters and $Q$ is be the sum of areas of all the triangles formed in this process, then:
→
The locus of the moving point $P$, such that $2PA = \,3PB$ where $A$ is $(0,0)$ and $B$ is $(4,-3)$, is
→