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

Question

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 (A) 1 / 247 (B) 2 / 247 (C) 4 / 741 (D) 5 / 741

Tardigrade Admin · Accepted Answer

Given, 7 a-9 b=0 or b=(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 C2=4 / 741.

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

$1/247$

$2/247$

$4/741$

$5/741$

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 $4/^{39} C_{2} = 4/741$ .

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

1/247

2/247

4/741

5/741