From the set {1, 2, 3, 4, 5}, two numbers a and b(a b) are chosen at random. The probability that a/b is an integer is:

Question

From the set {1, 2, 3, 4, 5}, two numbers $a$ and $b (a \neq b)$ are chosen at random. The probability that $\frac{a}{b}$ is an integer is:

Smart Achievers · Accepted Answer

(2)

Ans. $\frac{1}{4}$

Explanation:

Total possible outcomes of $(a, b)$ = {(1,2), (1,3), (1,4), (1,5), (2,1), (2,3), (2,4), (2,5), (3,1), (3,2), (3,4), (3,5), (4,1), (4,2), (4,3), (4,5), (5,1), (5,2), (5,3), (5,4)}

$\Rightarrow$ Number of possible outcomes = 20

Also, favourable outcomes of $(a, b)$ = {(2,1), (3,1), (4,1), (4,2), (5,1)}

$\Rightarrow$ Number of favourable outcomes = 5

$∴$ $P (\frac{a}{b} is integer) = \frac{5}{20} = \frac{1}{4}$

Solution

Q.
From the set {1, 2, 3, 4, 5}, two numbers $a$ and $b (a \neq b)$ are chosen at random. The probability that $\frac{a}{b}$ is an integer is:

1 $\frac{1}{3}$

2 $\frac{1}{4}$

3 $\frac{1}{2}$

4 $\frac{3}{5}$

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Solution

Q. From the set {1, 2, 3, 4, 5}, two numbers a and b (a≠b) are chosen at random. The probability that ab is an integer is:

1 13

2 14

3 12