First slide

Introduction to probability

Question

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

Moderate

A

$\frac{1}{247}$
B

$\frac{2}{247}$
C

$\frac{4}{741}$
D

$\frac{5}{741}$

Solution

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 $\frac{4}{39_{C_{2}}} = \frac{4}{741}$

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