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

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) (1/742) (B) (4/743) (C) (4/741) (D) (5/741)

Tardigrade Admin · Accepted Answer

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}

Q. 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

$\frac{1}{742}$

$\frac{4}{743}$

$\frac{4}{741}$

$\frac{5}{741}$

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,
$= \frac{4}{^{39} C _{2}} = \frac{4}{741}$

Q. 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

7421​

7434​

7414​

7415​