Two numbers x and y are chosen at random from | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) The total number of ways to choose two distinct numbers $x$ and $y$ from the set $\{1, 2, \dots, 15\}$ is $15 	imes 14 = 210$.The equation of the

Vedclass · Accepted Answer

$\frac{1}{42}$

Vedclass · Answer

(D) The total number of ways to choose two distinct numbers $x$ and $y$ from the set $\{1, 2, \dots, 15\}$ is $15 	imes 14 = 210$.The equation of the line passing through $(0, 0)$ with a slope of $\frac{2}{3}$ is $y = \frac{2}{3}x$,which simplifies to $2x = 3y$.We need to find pairs $(x, y)$ such that $x, y \in \{1, 2, \dots, 15\}$ and $2x = 3y$. This implies $x$ must be a multiple of $3$. Let $x = 3k$,then $2(3k) = 3y$,so $y = 2k$.For $k=1, x=3, y=2$.For $k=2, x=6, y=4$.For $k=3, x=9, y=6$.For $k=4, x=12, y=8$.For $k=5, x=15, y=10$.There are $5$ such favorable pairs.The probability is $\frac{5}{210} = \frac{1}{42}$.

Box	White	Black
$B_1$	$1$	$2$
$B_2$	$3$	$1$
$B_3$	$2$	$3$

Two numbers $x$ and $y$ are chosen at random from the set of integers $\{1, 2, 3, 4, \dots, 15\}$. The probability that the point $(x, y)$ lies on a line passing through $(0, 0)$ with a slope of $\frac{2}{3}$ is:

Similar Questions

Let $\Omega$ be the sample space and $A \subseteq \Omega$ be an event. Given below are two statements:
$(S1) : \text{If } P(A) = 0, \text{ then } A = \phi$
$(S2) : \text{If } P(A) = 1, \text{ then } A = \Omega$
Then:

Two dice are thrown three times. What is the probability that the first throw shows $10$,the second throw shows $11$,and the third throw shows $12$?

Two dice are thrown simultaneously. The probability of obtaining a total score of $5$ is

The probability that a non-leap year contains $53$ Sundays is

Boxes $B_1, B_2$,and $B_3$ contain balls as given below:
Box White Black
$B_1$ $1$ $2$
$B_2$ $3$ $1$
$B_3$ $2$ $3$

One ball is drawn at random from each box. Then,among the balls drawn,the probability that two are black and one is white,is

Vedclass Test Series

Exam Paper Generator

Online Exam Module