In a single throw of two dice , what is the probability of
at least one ace

Answer

To find the probability of getting at least one ace (which is a 1) 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:
\[ \text{Total outcomes} = 6 \times 6 = 36 \]

### Step 2: Find the number of favorable outcomes for at least one ace
To find the number of outcomes that include at least one ace (1), we can list the combinations where at least one die shows a 1.

The combinations are:
- (1,1)
- (1,2)
- (1,3)
- (1,4)
- (1,5)
- (1,6)
- (2,1)
- (3,1)
- (4,1)
- (5,1)
- (6,1)

Counting these combinations, we find that there are 11 outcomes where at least one die shows a 1.

### Step 3: Calculate the probability
The probability of an event is given by the formula:
\[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]
Substituting in our values:
\[ \text{Probability of at least one ace} = \frac{11}{36} \]

### Final Answer
Thus, the probability of getting at least one ace when throwing two dice is:
\[ \frac{11}{36} \]

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