Out of 100 days, the forecast predicted by the wheather department proved to be true on 20 days chosen any one day from these 100 days. The probability that the forecast proved to be false is ..........

Options

A. `1/3`
B. `1/4`
C. `3/4`
D. `4/5`

Answer

To solve the problem step by step, we will follow the logical reasoning based on the information provided.

### Step-by-Step Solution:

1. **Understand the Total Days and True Forecasts**:
- We know that the weather forecast was accurate for 20 days out of a total of 100 days.

2. **Calculate the Number of False Forecasts**:
- To find the number of days the forecast was false, we subtract the number of true forecasts from the total number of days:
\[ \text{Number of false forecasts} = \text{Total days} - \text{Number of true forecasts} \]
\[ \text{Number of false forecasts} = 100 - 20 = 80 \]

3. **Use the Probability Formula**:
- The formula for probability is given by:
\[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} \]
- In this case, the favorable outcome is the number of false forecasts (80), and the total outcomes are the total number of days (100).

4. **Substitute the Values into the Formula**:
- Now we can substitute the values into the probability formula:
\[ \text{Probability that the forecast proved to be false} = \frac{80}{100} \]

5. **Simplify the Fraction**:
- To simplify \(\frac{80}{100}\):
\[ \frac{80 \div 20}{100 \div 20} = \frac{4}{5} \]

6. **Convert to Decimal (if needed)**:
- The fraction \(\frac{4}{5}\) can also be expressed as a decimal:
\[ \frac{4}{5} = 0.8 \]

### Final Answer:
The probability that the forecast proved to be false is \(\frac{4}{5}\) or \(0.8\).

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