A bag contains 5 brown and 4 white socks. A man pulls out two soc… - Vidyadip

MCQ

A bag contains $5$ brown and $4$ white socks. A man pulls out two socks. The probability that these are of the same colour is

A
$\frac{5}{{108}}$
B
$\frac{{18}}{{108}}$
C
$\frac{{30}}{{108}}$
✓
$\frac{{48}}{{108}}$

✓

Answer

Correct option: D.

$\frac{{48}}{{108}}$

d
(d) Total socks $ = 5 + 4 = 9$

The number of ways to select $2$ socks out of $9$ = $^9{C_2}$

If number of ways to select both brown socks $ = {\,^5}{C_2}$

And number of ways to select both white socks $ = {\,^4}{C_2}$

$\therefore \,P$ (Both brown or white) $ = \frac{{^5{C_2} + {\,^4}{C_2}}}{{^9{C_2}}} = \frac{{16}}{{36}} = \frac{{48}}{{108}}$.

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

Three points $\mathrm{O}(0,0), \mathrm{P}\left(\mathrm{a}, \mathrm{a}^2\right), \mathrm{Q}\left(-\mathrm{b}, \mathrm{b}^2\right), \mathrm{a}>0, \mathrm{~b}>0$, are on the parabola $y=x^2$. Let $S_1$ be the area of the region bounded by the line $P Q$ and the parabola, and $S_2$ be the area of the triangle $O P Q$. If the minimum value of $\frac{\mathrm{S}_1}{\mathrm{~S}_2}$ is $\frac{\mathrm{m}}{\mathrm{n}}, \operatorname{gcd}(\mathrm{m}, \mathrm{n})=1$, then $\mathrm{m}+\mathrm{n}$ is equal to :

If $f(x)$ is a differentiable function such that $f:R \to r$ and $f\left( {\frac{1}{n}} \right) = 0\;\forall \;n \ge 1,n \in I$ then

If $2x - 4y = 9$ and $6x - 12y + 7 = 0$ are the tangents of same circle, then its radius will be

Let $t_n$ denote the number of integral-sided triangles with distinct sides chosen from $\{1,2,3, \ldots, n\}$. Then, $t_{20}-t_{19}$ equals

If ${ }^{20} \mathrm{C}_{\mathrm{r}}$ is the co-efficient of $\mathrm{x}^{\mathrm{r}}$ in the expansion of $(1+x)^{20}$, then the value of $\sum_{r=0}^{20} r^{2}\,\,{ }^{20} C_{r}$ is equal to :

Let $X=\{x \in R: \cos (\sin x)=\sin (\cos x)\} .$ The number of elements in $X$ is

Let a triangle be bounded by the lines $L _{1}: 2 x +5 y =10$; $L _{2}:-4 x +3 y =12$ and the line $L _{3}$, which passes through the point $P (2,3)$, intersect $L _{2}$ at $A$ and $L _{1}$ at $B$. If the point $P$ divides the line-segment $A B$, internally in the ratio $1: 3$, then the area of the triangle is equal to

Let $A$ be the sum of the first $20$ terms and $B$ be the sum of the first $40$ terms of the series ${1^2} + 2 \cdot {2^2} + {3^2} + 2 \cdot {4^2} + {5^2} +.......$ If $B - 2A = 100\lambda $ then $\lambda $ is equal to :

If $f(x) = {\cos ^{ - 1}}\left[ {{{1 - {{(\log x)}^2}} \over {1 + {{(\log x)}^2}}}} \right]\,,$ then the value of $f'(e) = $

If ${x^2} + {y^2} = t - {1 \over t},$ ${x^4} + {y^4} = {t^2} + {1 \over {{t^2}}}$, then ${x^3}y{{dy} \over {dx}} = $