In a single throw of two dice , find the probability of getting a total of 10 or 11.

Answer

To solve the problem of finding the probability of getting a total of 10 or 11 when throwing two dice, we can follow these steps:

### Step 1: Determine the total number of outcomes
When throwing two dice, each die has 6 faces. Therefore, the total number of outcomes when throwing two dice is:
\[ 6 \times 6 = 36 \]

### Step 2: Identify the favorable outcomes for a total of 10
Next, we need to find the combinations of the two dice that give a total of 10. The pairs that yield a sum of 10 are:
- (4, 6)
- (5, 5)
- (6, 4)

Thus, the favorable outcomes for a total of 10 are:
1. (4, 6)
2. (5, 5)
3. (6, 4)

This gives us a total of **3 favorable outcomes** for a total of 10.

### Step 3: Identify the favorable outcomes for a total of 11
Now, we find the combinations of the two dice that give a total of 11. The pairs that yield a sum of 11 are:
- (5, 6)
- (6, 5)

Thus, the favorable outcomes for a total of 11 are:
1. (5, 6)
2. (6, 5)

This gives us a total of **2 favorable outcomes** for a total of 11.

### Step 4: Calculate the total favorable outcomes
Now, we add the favorable outcomes for both totals:
\[ \text{Total favorable outcomes} = \text{Favorable outcomes for 10} + \text{Favorable outcomes for 11} = 3 + 2 = 5 \]

### Step 5: Calculate the probability
The probability \( P \) of getting a total of 10 or 11 is given by the formula:
\[ P = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{5}{36} \]

### Final Answer
The probability of getting a total of 10 or 11 when throwing two dice is:
\[ \frac{5}{36} \]

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