Two dice are thrown at the same time. Write down all the possible outcomes. Find the probability of getting the sum of two numbers appearing on the top of the dice as:
less than 13

Answer

To solve the problem step by step, we will follow these instructions:

### Step 1: Identify the possible outcomes when two dice are thrown.
When two dice are thrown, each die has 6 faces, numbered from 1 to 6. The outcomes can be represented as pairs (x, y) where x is the result from the first die and y is the result from the second die.

### Step 2: List all the possible outcomes.
The possible outcomes can be listed in a systematic way:

- For die 1 showing 1: (1,1), (1,2), (1,3), (1,4), (1,5), (1,6)
- For die 1 showing 2: (2,1), (2,2), (2,3), (2,4), (2,5), (2,6)
- For die 1 showing 3: (3,1), (3,2), (3,3), (3,4), (3,5), (3,6)
- For die 1 showing 4: (4,1), (4,2), (4,3), (4,4), (4,5), (4,6)
- For die 1 showing 5: (5,1), (5,2), (5,3), (5,4), (5,5), (5,6)
- For die 1 showing 6: (6,1), (6,2), (6,3), (6,4), (6,5), (6,6)

Thus, the complete list of outcomes is:
1. (1,1), (1,2), (1,3), (1,4), (1,5), (1,6)
2. (2,1), (2,2), (2,3), (2,4), (2,5), (2,6)
3. (3,1), (3,2), (3,3), (3,4), (3,5), (3,6)
4. (4,1), (4,2), (4,3), (4,4), (4,5), (4,6)
5. (5,1), (5,2), (5,3), (5,4), (5,5), (5,6)
6. (6,1), (6,2), (6,3), (6,4), (6,5), (6,6)

### Step 3: Calculate the total number of possible outcomes.
Since each die has 6 faces, the total number of outcomes when two dice are thrown is:
\[ 6 \times 6 = 36 \]

### Step 4: Determine the probability of getting a sum less than 13.
The maximum sum that can be obtained when throwing two dice is \(6 + 6 = 12\). Therefore, all possible outcomes will have a sum less than 13.

### Step 5: Calculate the probability.
The probability \(P\) of an event is given by the formula:
\[ P = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]
In this case, the number of favorable outcomes (sum less than 13) is 36 and the total number of outcomes is also 36.

Thus,
\[ P = \frac{36}{36} = 1 \]

### Final Answer:
The probability of getting the sum of two numbers appearing on the top of the dice as less than 13 is **1**.

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