A dice is thrown once. Find the probability of getting :
a number between 2 and 6.

Answer

To solve the problem of finding the probability of getting a number between 2 and 6 when a die is thrown once, we can follow these steps:

### Step 1: Identify the Sample Space
When a die is thrown, the possible outcomes (sample space) are:
\[ S = \{1, 2, 3, 4, 5, 6\} \]

### Step 2: Determine the Favorable Outcomes
We need to find the numbers that are between 2 and 6. The numbers that fit this criterion are:
\[ \{3, 4, 5\} \]
Thus, the favorable outcomes are 3, 4, and 5.

### Step 3: Count the Total Outcomes
The total number of outcomes when throwing a die is 6 (the numbers 1 through 6).

### Step 4: Count the Favorable Outcomes
The number of favorable outcomes (the numbers between 2 and 6) is 3 (which are 3, 4, and 5).

### Step 5: Calculate the Probability
The probability \( P \) of an event is given by the formula:
\[ P(\text{event}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]
Substituting the values we have:
\[ P(\text{getting a number between 2 and 6}) = \frac{3}{6} \]

### Step 6: Simplify the Probability
We can simplify \( \frac{3}{6} \):
\[ P = \frac{1}{2} \]

Thus, the probability of getting a number between 2 and 6 when a die is thrown once is:
\[ \frac{1}{2} \]

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