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?
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 $\frac{2}{3}$.