14.Probability
normal

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

A

$\frac{1}{3}$

B

$\frac{1}{15}$

C

$\frac{1}{21}$

D

$\frac{1}{42}$

Solution

Total cases $\Rightarrow \quad^{15} \mathrm{C}_{2} .2 !=15.14$

$2 \mathrm{x}=3 \mathrm{y} \Rightarrow(3,2),(6,4),(9,6),(12,8),(15,10)$

Fovourable cases $=5$

Probability $=\frac{5}{15.14}=\frac{1}{42}$

Standard 11
Mathematics

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