In the city where the Absent-Minded Scholar lives, telephone numbers consist of 7 digits. The Scholar easily remembers a telephone number if it is a palindrome, that is, it reads the same from left to right as from right to left. For example, the number 4435344 is easily remembered by the Scholar because it is a palindrome. The number 3723627 is not a palindrome, so the Scholar has difficulty remembering such a number. Find the probability that the telephone number of a new random acquaintance will be easily remembered by the Scholar.
As is known, the first digit of a phone number can't be just any digit. Let the number of allowed first digits be $m$. Then the total number of phone numbers is $m \cdot 10^{6}$. An easy-to-remember number (one that is easily memorized) is uniquely determined by its first four digits. Therefore, the total number of seven-digit palindromes is $m \cdot 10^{3}$. Thus, the probability that a randomly selected number will be easy to remember is $\frac{m \cdot 10^{3}}{m \cdot 10^{6}}=0.001$.

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