If two numbers $a$ and $b$ are chosen from the set of integers 1 to 39 , then the probability that those…
If two numbers $a$ and $b$ are chosen from the set of integers 1 to 39 , then the probability that those numbers satisfy the equation $7 a-9 b=0$ is
$\frac{1}{742}$
$\frac{4}{743}$
$\frac{4}{741}$
$\frac{5}{741}$
Solution
Sample space for choosing two numbers from set of integers 1 to $39={ }^{39} C_2$
Favourable elementary events are
$
(a, b)=(9,7),(18,14),(27,21),(36,28)
$
So, probability to satisfy the equation $7 a-9 b=0$ is,
$
=\frac{4}{{ }^{39} C_2}=\frac{4}{741} .
$