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1. Non-leap years between 1801 and 1900 ●○○○○ 10 ptsHow many non-leap years are there from 1801 to 1900 inclusive, in the Gregorian calendar?
2. Birthday not in December ●○○○○ 10 ptsIgnoring leap years, what is the probability that a randomly chosen person's birthday is not in December? Give your answer as a decimal rounded to three decimal places.
3. Months with five Fridays ●●○○○ 20 ptsOne year, January 1 and April 1 were both on a Thursday. How many months in that year have five Fridays? Justify your answer.
4. Maximum leap years in 150 years ●●○○○ 20 ptsIn a calendar system in which leap years occur every four years, with no exceptions, what is the maximum possible number of leap years in a 150-year period?
5. Birthday match among three people ●●○○○ 20 ptsThree people are in a room. Assuming each birthday is equally likely among 365 days (ignore leap years), find the probability that at least two of them share the same birthday. Round your answer to 9 decimal places.
6. Smallest group with a shared birthday ●●●○○ 50 ptsWhat is the smallest number of people in a group such that the probability that at least two of them share the same birthday is greater than 50%? Assume there are 365 equally likely birthdays and ignore leap years.
7. Five Sundays in February ●●●○○ 50 ptsApril 16, 2011 was a Saturday. Find all years in the 21st century (2001–2100) in which February has five Sundays.
8. Minimum people covering every birthday ●●●●○ 100 ptsAssume a year has 365 equally likely birthdays, each person's birthday is independent of the others, and leap years are ignored. What is the minimum number of people needed so that the probability that every one of the 365 days is someone's birthday is greater than $0.5$?