A die is thrown once . Find the probability of getting any number lying between 2 and 5 .

Answer

To solve the problem of finding the probability of getting any number lying between 2 and 5 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: Define the Favorable Outcomes
We need to find the numbers that lie between 2 and 5. The numbers that meet this condition are:
\[ \{3, 4\} \]
So, the favorable outcomes are 3 and 4.

### Step 3: Count the Total Outcomes
The total number of outcomes when throwing a die is:
\[ n(S) = 6 \]

### Step 4: Count the Favorable Outcomes
The number of favorable outcomes (numbers between 2 and 5) is:
\[ n(F) = 2 \] (which are 3 and 4)

### Step 5: Calculate the Probability
The probability \( P \) of an event is given by the formula:
\[ P(E) = \frac{n(F)}{n(S)} \]
Substituting the values we found:
\[ P(\text{getting a number between 2 and 5}) = \frac{2}{6} = \frac{1}{3} \]

### Final Answer
The probability of getting any number lying between 2 and 5 when a die is thrown once is:
\[ \frac{1}{3} \]

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