5. Easy Numbers. In the city where the Absent-Minded Scientist lives, telephone numbers consist of 7 digits. The Scientist easily remembers a telephone number if the number is a palindrome, that is, it reads the same from left to right and from right to left.

For example, the number 4435344 the Scientist remembers easily, because this number is a palindrome. The number 3723627 is not a palindrome, so the Scientist has difficulty remembering such a number. Find the probability that the telephone number of a new random acquaintance the Scientist will remember easily.
Solution. 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 numbers is $m \cdot 10^{6}$. A palindromic number is uniquely determined by its first four digits. Therefore, the number of seven-digit palindromes is $m \cdot 10^{3}$.

Thus, the probability that a random number will be a palindrome is

$$
\mathrm{P}=\frac{m \cdot 10^{3}}{m \cdot 10^{6}}=0.001
$$

Answer: 0.001.