Question 1

We will list all the possible results when a die is rolled.

Step 1 — List all outcomes

Let's consider a standard 6-sided die. Each side has a number from 1 to 6. When we roll the die, one side will face up. The possible numbers that can face up are 1, 2, 3, 4, 5, or 6. We call the set of all possible outcomes the sample space (S).

$S = \{1, 2, 3, 4, 5, 6\}$

Step 2 — Count the outcomes

Now, let's count how many outcomes are in our sample space. The number of elements in the sample space is denoted as $n(S)$.

$n(S) = \text{number of elements in } S$

$n(S) = 6$

$\boxed{\text{Total outcomes} = 6}$

Answer

(i) The total number of possible outcomes in the sample space is 6.