Solution. Maxim could have been born on any day starting from September 2, 2007, and ending on August 31, 2008. In total, there are 365 days, considering that 2008 was a leap year with February 29. Assuming that all days are equally likely (we have no information suggesting otherwise), we find the desired probability:

$$
\frac{31+29+31+30+31+30+31+31}{365}=\frac{244}{365} \approx \frac{2}{3}
$$

Answer: $\frac{244}{365}$, which is slightly more than $\frac{2}{3}$.
5. First-grader (6th grade. 2 points). Maksim will go to the first grade on September 1, 2014, at the age of 6 years, and this day will not be his birthday. What is the probability that he was born in 2008?