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:
10

Answer

To solve the problem of finding the probability of getting a sum of 10 when two dice are thrown, we will follow these steps:

### Step 1: List all possible outcomes when two dice are thrown.
When two dice are thrown, each die has 6 faces. Therefore, the total number of possible outcomes is:
\[ 6 \times 6 = 36 \]
The possible outcomes can be represented as ordered pairs \((a, b)\), where \(a\) is the result from the first die and \(b\) is the result from the second die. The outcomes are:
\[ (1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (2,4), (2,5), (2,6), (3,1), (3,2), (3,3), (3,4), (3,5), (3,6), (4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (5,1), (5,2), (5,3), (5,4), (5,5), (5,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6) \]

### Step 2: Identify the outcomes that give a sum of 10.
Next, we need to find the pairs \((a, b)\) where the sum \(a + b = 10\):
- \( (4, 6) \)
- \( (5, 5) \)
- \( (6, 4) \)

Thus, the outcomes that result in a sum of 10 are:
1. \( (4, 6) \)
2. \( (5, 5) \)
3. \( (6, 4) \)

### Step 3: Count the favorable outcomes.
From the above, we see that there are 3 favorable outcomes.

### Step 4: Calculate the probability.
The probability \(P\) of an event is given by the formula:
\[ P = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]
Substituting the values we found:
\[ P = \frac{3}{36} = \frac{1}{12} \]

### Final Answer:
The probability of getting a sum of 10 when two dice are thrown is \(\frac{1}{12}\).

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