Two numbers ' a ' and ' b ' are selected successively one after another without replacement from the integers 1 to 15 . What is the probability that (a/b) will be an integer?

Question

Two numbers ' a ' and ' b ' are selected successively one after another without replacement from the integers 1 to 15 . What is the probability that (a/b) will be an integer? (A) (5/7) (B) (3/7) (C) (2/7) (D) (1/7)

Tardigrade Admin · Accepted Answer

Let b=1, then a=2 to 15 . Let b=2, then a=4,6, ldots, 14. In this way, find numbers a and b such that (a/b) is the integer.

Q. Two numbers ' $a$ ' and ' $b$ ' are selected successively one after another without replacement from the integers 1 to 15 . What is the probability that $\frac{a}{b}$ will be an integer?

$\frac{5}{7}$

$\frac{3}{7}$

$\frac{2}{7}$

$\frac{1}{7}$

Let $b = 1$ , then $a = 2$ to 15 .
Let $b = 2$ , then $a = 4, 6, \dots, 14$ .
In this way, find numbers $a$ and $b$ such that $\frac{a}{b}$ is the integer.

Q. Two numbers ' a ' and ' b ' are selected successively one after another without replacement from the integers 1 to 15 . What is the probability that ba​ will be an integer?

75​

73​

72​

71​