There are 10 marbles in a box which are marked with the distinct numbers from 1 to 10. If a marble is drawn, then what is the probability of getting a marble being a odd number less than 8?

Answer

To solve the problem of finding the probability of drawing a marble that is an odd number less than 8 from a box of 10 marbles marked with distinct numbers from 1 to 10, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Total Outcomes:**
The total number of marbles in the box is 10, as they are marked with the numbers 1 to 10.
- **Total Outcomes = 10**

2. **Identify the Favorable Outcomes:**
We need to find the odd numbers that are less than 8. The odd numbers from 1 to 10 are:
- 1, 3, 5, 7, 9
Now, we filter these to find which are less than 8:
- The odd numbers less than 8 are: 1, 3, 5, and 7.
- **Favorable Outcomes = 4** (1, 3, 5, 7)

3. **Apply the Probability Formula:**
The formula for probability is given by:
\[ \text{Probability} = \frac{\text{Number of Favorable Outcomes}}{\text{Total Outcomes}} \]
Substituting the values we found:
\[ \text{Probability} = \frac{4}{10} \]

4. **Simplify the Fraction:**
To simplify \(\frac{4}{10}\), we divide both the numerator and the denominator by their greatest common divisor, which is 2:
\[ \frac{4 \div 2}{10 \div 2} = \frac{2}{5} \]

5. **Final Answer:**
The probability of drawing a marble that is an odd number less than 8 is:
\[ \frac{2}{5} \]