In a lottery there are 20 prizes and 15 blanks. What is the probability of getting prize ?

Options

A. `1/10`
B. `2/5`
C. `4/7`
D. `2/7`

Answer

To solve the problem of finding the probability of getting a prize in a lottery with 20 prizes and 15 blanks, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Number of Desired Outcomes**:
- In this case, the desired outcome is winning a prize. There are 20 prizes available.
- **Desired Outcomes = 20** (the number of prizes).

2. **Identify the Total Number of Possible Outcomes**:
- The total outcomes include both the prizes and the blanks.
- There are 20 prizes and 15 blanks, so we add these together.
- **Total Outcomes = 20 (prizes) + 15 (blanks) = 35**.

3. **Apply the Probability Formula**:
- The probability \( P \) of an event is given by the formula:
\[ P = \frac{\text{Number of Desired Outcomes}}{\text{Total Possible Outcomes}} \]
- Substituting the values we found:
\[ P = \frac{20}{35} \]

4. **Simplify the Fraction**:
- To simplify \( \frac{20}{35} \), we can divide both the numerator and the denominator by their greatest common divisor, which is 5.
- Thus:
\[ P = \frac{20 \div 5}{35 \div 5} = \frac{4}{7} \]

5. **Conclusion**:
- The probability of getting a prize in this lottery is \( \frac{4}{7} \).

### Final Answer:
The probability of getting a prize is \( \frac{4}{7} \).