In a single throw of two dice, what is the probability of getting
five on one die and six on the other

Answer

To find the probability of getting a five on one die and a six on the other when throwing two dice, we can follow these steps:

### Step 1: Determine the total number of outcomes
When two dice are thrown, each die has 6 faces. Therefore, the total number of outcomes when throwing two dice is calculated as:
\[ \text{Total outcomes} = 6 \times 6 = 36 \]

### Step 2: Identify the favorable outcomes
We need to find the outcomes where one die shows a five and the other die shows a six. There are two favorable outcomes:
1. The first die shows a five and the second die shows a six: (5, 6)
2. The first die shows a six and the second die shows a five: (6, 5)

Thus, the number of favorable outcomes (NF) is:
\[ \text{Number of favorable outcomes} = 2 \]

### Step 3: Calculate the probability
The probability (P) of an event is given by the formula:
\[ P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]
Substituting the values we found:
\[ P(E) = \frac{2}{36} \]

### Step 4: Simplify the probability
Now, we can simplify the fraction:
\[ P(E) = \frac{2}{36} = \frac{1}{18} \]

### Final Answer
The probability of getting a five on one die and a six on the other is:
\[ \frac{1}{18} \]

---