The record of a weather station shows that out of the past 250 consecutive days, its weather forecasts were correct 175 times.
What is the probability that on a given day it was correct.

Answer

To find the probability that the weather forecast was correct on a given day, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Total Number of Days**:
The total number of days recorded is 250.

2. **Identify the Number of Correct Forecasts**:
The number of times the weather forecast was correct is 175.

3. **Use the Probability Formula**:
The probability (P) of an event is given by the formula:
\[ P(\text{event}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]
In this case, the favorable outcome is the number of days the forecast was correct (175), and the total outcomes are the total number of days (250).

4. **Substitute the Values into the Formula**:
\[ P(\text{correct forecast}) = \frac{175}{250} \]

5. **Simplify the Fraction**:
To simplify \(\frac{175}{250}\), we can divide both the numerator and the denominator by their greatest common divisor (GCD), which is 25:
\[ \frac{175 \div 25}{250 \div 25} = \frac{7}{10} \]

6. **Convert to Decimal**:
To express \(\frac{7}{10}\) as a decimal, we divide 7 by 10:
\[ \frac{7}{10} = 0.7 \]

7. **Conclusion**:
Therefore, the probability that the weather forecast was correct on a given day is:
\[ P(\text{correct forecast}) = 0.7 \]

### Final Answer:
The probability that the weather forecast was correct on a given day is **0.7**.

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