Question

What is the sample space of rolling a $6$ sided die?

Answer 1

Hint: In this problem they have asked to calculate the sample space of the $6$ sided die. We know that the sample space is the set of possible outcomes for the given event. In the problem we have given the event of rolling a $6$ sided die. So, we see how many faces are there for a six-sided die and list all the possible outcomes when the die is rolled.

Complete step by step answer:
Given that a six-sided die is rolled.
We can observe that a six-sided row is in the shape of a cuboid shape which is nothing but a three-dimensional square.
We know that the square is a polygon having four sides and one plane. When we extrude a square into a three-dimensional shape, the four sides of the square will form four planes in the three-dimensional coordinate system and the plane of the square is also mirrored to another side.
Totally we have $4+2=6$ planes for a cuboid shaped die or six-sided die.
Let us give the numbering for the planes from $1$ to $6$. When we roll a die there may be chances for coming $1$ or $2$ or $3$ or $4$ or $5$ or $6$.

Hence the sample space of six-sided die is $\left\{ 1,2,3,4,5,6 \right\}$.

Note: In this problem we have only asked to calculate the sample space so we have calculated the probable outcomes only. If they have asked to calculate the sample space distribution then we need to calculate the probabilities of each event in the sample space.