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14.Probability
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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