Q77 / 160 · AP EAMCET 2018 (24 Apr Shift 1) · Mathematics

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

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

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, $$ =\frac{4}{{ }^{39} C_2}=\frac{4}{741} . $$

Hence, the correct answer is option: 'C'.

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