A dice is thrown two times.describe sample space

Explanation

To describe the sample space when a die is thrown two times, we can follow these steps:

### Step 1: Understand the outcomes of a single die throw
When a single die is thrown, there are 6 possible outcomes:
- 1
- 2
- 3
- 4
- 5
- 6

### Step 2: Determine the total outcomes for two throws
When the die is thrown two times, each throw is independent of the other. Therefore, the total number of outcomes when throwing the die twice is calculated as:
\[ \text{Total Outcomes} = 6 \times 6 = 36 \]

### Step 3: List the sample space
The sample space consists of all possible ordered pairs (outcomes) from the two throws. We can represent this as (first throw, second throw).

The sample space can be listed as follows:
- For the first throw of 1: (1,1), (1,2), (1,3), (1,4), (1,5), (1,6)
- For the first throw of 2: (2,1), (2,2), (2,3), (2,4), (2,5), (2,6)
- For the first throw of 3: (3,1), (3,2), (3,3), (3,4), (3,5), (3,6)
- For the first throw of 4: (4,1), (4,2), (4,3), (4,4), (4,5), (4,6)
- For the first throw of 5: (5,1), (5,2), (5,3), (5,4), (5,5), (5,6)
- For the first throw of 6: (6,1), (6,2), (6,3), (6,4), (6,5), (6,6)

### Step 4: Compile the complete sample space
The complete sample space can be summarized as:
\[ S = \{ (1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (2,4), (2,5), (2,6), (3,1), (3,2), (3,3), (3,4), (3,5), (3,6), (4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (5,1), (5,2), (5,3), (5,4), (5,5), (5,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6) \} \]