What is the probability that a leap year selected at random will have 53 Sundays?
Instruction: Determine the probability of a randomly chosen leap year having 53 Sundays.
Updated
Example Answer
A leap year has 366 days: 52 complete weeks and two additional days. The weekdays of January 1 and January 2 therefore occur 53 times. Sunday occurs 53 times exactly when January 1 is Saturday or Sunday.
If the intended model makes each starting weekday equally likely, two of the seven starting weekdays qualify, giving 2/7, or about 28.6%. I would state that assumption because choosing an actual Gregorian leap year uniformly does not make its starting weekday exactly uniform.
Calendar check
For a leap year chosen uniformly from the 97 leap years in a complete Gregorian 400-year cycle, 13 start on Saturday and 15 on Sunday. The probability is therefore 28/97, about 28.9%. A different finite range should be counted directly.
If January 1 is Sunday, its Sundays are days 1, 8, …, 365; day 366 is Monday. If January 1 is Saturday, its Sundays are days 2, 9, …, 366.
Why this works
The weekday count is exact; the probability depends on how the leap year is sampled.