In Hungarian license plates, the digits can also be the same. Based on their observations, someone claimed that on average, nearly 3 out of 10 vehicles have such a license plate. Is this statement true?
Solution. The numeric part of a Hungarian car license plate is a three-digit number ranging from 001 to 999. We do not consider the letter part, as for a given event, the ratio of favorable outcomes to total outcomes does not change due to the letters. There are 999 numbers from 001 to 999, and among them, the number of three-digit numbers without repetition is the number of third-class variations of the digits $0,1,2, \ldots, 9$: $V_{10}^{3}=10 \cdot 9 \cdot 8=720$.

Therefore, there are $999-720=279$ three-digit numbers where at least two digits are repeated. Let $A$ be the event that the observed license plate number contains at least two identical digits. Then $p(A)=\frac{279}{999} \approx 0.28$.

The observer tried to calculate the relative frequency of event $A$, which should be close to $p(A)$ if they observed "enough" vehicles. According to the statement, the frequency is $\frac{3}{10}=0.3$. The value 0.28 is close to this, so the statement is true.