1. (10 points) In one of the regions on the planet, seismic activity was studied. 80 percent of all days were quiet. The instrument predictions promised a calm situation in 64 out of 100 cases; moreover, in 70 percent of all cases when the day was quiet, the instrument predictions came true. What percentage of days with increased seismic activity are those in which the predictions did not match reality?
Solution. Let the total number of observed days be x. The number of actually quiet days was $0.8x$, and seismically active days were $0.2x$. The predictions of quiet days matched the actually quiet days: $0.7 \cdot 0.8x = 0.56x$. Then the number of active days that did not match the predictions was $0.64x - 0.56x = 0.08x$, and $\frac{0.08x}{0.2x} \cdot 100\% = 40\%$.

Answer: $40\%$

## Criteria

| Points | Conditions for Awarding |
| :---: | :--- |
| 10 points | Fully justified solution |
| 5 points | An arithmetic error was made with correct reasoning or insufficiently justified solution |
| 0 points | Incorrect reasoning or only the answer is written. |