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  4. Two numbers a, b are chosen from the set of integers 1,2,3, ldots, 39. Then probability that the equation 7 a-9 b =0 is satisfied is

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Q. Two numbers $a, b$ are chosen from the set of integers $1,2,3, \ldots, 39$. Then probability that the equation $7 a-9 b$ $=0$ is satisfied is

Probability

Solution:

Given,
$7 a-9 b=0 $ or $ b=\frac{7}{9} a$
Hence, number of pairs $(a, b)$ can be $(9,7) ;(18,14) ;(27,21)$; $(36,28)$. Hence, the required probability is $4 /{ }^{39} C_{2}=4 / 741$.