Question

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 $7a - 9b = 0$ is

• A. $\frac{1}{742}$
• B. $\frac{4}{743}$
• C. $\frac{4}{741}$
• D. $\frac{5}{741}$

Answer 1

Answer: (C)

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} $