A die is thrown once. Find the probability that number turns up on the upper face is greater than 2 and less than 5.

Answer

To solve the problem of finding the probability that the number on the upper face of a die is greater than 2 and less than 5, we can follow these steps:

### Step 1: Identify the total number of outcomes when throwing a die.
A standard die has 6 faces, which are numbered from 1 to 6. Therefore, the total number of possible outcomes when a die is thrown is:

Total outcomes = {1, 2, 3, 4, 5, 6}
Total outcomes = 6

### Step 2: Determine the favorable outcomes based on the condition.
We need to find the numbers that are greater than 2 and less than 5. The numbers that satisfy this condition are:

- Greater than 2: 3, 4, 5, 6
- Less than 5: 1, 2, 3, 4

The numbers that are both greater than 2 and less than 5 are:

Favorable outcomes = {3, 4}
Favorable outcomes = 2

### 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 the values we found:

\[ \text{Probability} = \frac{2}{6} \]

### Step 4: Simplify the fraction.
We can simplify the fraction:

\[ \frac{2}{6} = \frac{1}{3} \]

### Conclusion:
The probability that the number on the upper face of the die is greater than 2 and less than 5 is:

**Probability = \( \frac{1}{3} \)**

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