Question

A die is rolled. If $\mathrm{X}$ denotes the number of positive divisors of the outcomes then the range of the random variable $\mathrm{X}$ is

• A. $\{1,2,3\}$
• B. $\{1,2,3,4\}$
• C. $\{1,2,3,4,5,6\}$
• D. $\{1,3,5\}$

Answer 1

The correct option is B

$\{1,2,3,4\}$

Explanation of the correct option

If a die is rolled, the possible outcomes are $\{1,2,3,4,5,6\}$

Here, the random variable $\mathrm{X}$ is number of positive divisors of the outcomes.

Hence, the possible outcomes with their positive divisors are as follows:

Outcomes	Positive divisors	Number ($\mathrm{X}$)
$1$	$1$	$1$
$2$	$1,2$	$2$
$3$	$1,3$	$2$
$4$	$1,2,4$	$3$
$5$	$1,5$	$2$
$6$	$1,2,3,6$	$4$

Therefore, the range of the random variable $\mathrm{X}$ is $\{1,2,3,4\}$.

Hence, Option B is correct.