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 it was not correct on a given day ?

Answer

To find the probability that the weather forecast was not correct on a given day, we can follow these steps:

### Step-by-Step Solution:

1. **Identify Total Days and Correct Forecasts**:
- The total number of days recorded is 250.
- The number of days the forecast was correct is 175.

2. **Calculate the Number of Incorrect Forecasts**:
- To find the number of days the forecast was not correct, subtract the number of correct forecasts from the total days:
\[ \text{Incorrect forecasts} = \text{Total days} - \text{Correct forecasts} = 250 - 175 = 75 \]

3. **Use the Probability Formula**:
- The probability of an event is given by the formula:
\[ P(\text{Not Correct}) = \frac{\text{Number of Not Correct Forecasts}}{\text{Total Number of Forecasts}} \]
- Plugging in the values we have:
\[ P(\text{Not Correct}) = \frac{75}{250} \]

4. **Simplify the Fraction**:
- To simplify \(\frac{75}{250}\), we can divide both the numerator and the denominator by 25:
\[ P(\text{Not Correct}) = \frac{75 \div 25}{250 \div 25} = \frac{3}{10} \]

5. **Convert to Decimal**:
- Converting \(\frac{3}{10}\) to decimal form gives us:
\[ P(\text{Not Correct}) = 0.3 \]

### Final Answer:
The probability that the weather forecast was not correct on a given day is **0.3**.

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