The record of a weather station shows weather forecast of the past 250 consecutive days. Its weather forecasts were correct 175 times.
What is the probability that forecast 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 1: Identify the total number of days
The total number of days for which the weather forecasts were recorded is given as 250 days.

### Step 2: Determine the number of correct forecasts
According to the problem, the weather forecasts were correct 175 times.

### Step 3: Calculate the number of incorrect forecasts
To find the number of incorrect forecasts, we subtract the number of correct forecasts from the total number of days:
\[ \text{Number of incorrect forecasts} = \text{Total days} - \text{Correct forecasts} = 250 - 175 = 75 \]

### Step 4: Calculate the probability of an incorrect forecast
The probability of an event is calculated using the formula:
\[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]
In this case, the number of favorable outcomes (incorrect forecasts) is 75, and the total number of outcomes (total days) is 250. Thus, the probability that the forecast was not correct on a given day is:
\[ \text{Probability (not correct)} = \frac{75}{250} \]

### Step 5: Simplify the fraction
To simplify \(\frac{75}{250}\), we can divide both the numerator and the denominator by their greatest common divisor, which is 25:
\[ \frac{75 \div 25}{250 \div 25} = \frac{3}{10} \]

### Final Answer
The probability that the forecast was not correct on a given day is:
\[ \frac{3}{10} \]

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