What is the probability that a randomly chosen year is a leap year?

Instruction: Consider the Gregorian calendar rules for leap years.

Context: This question assesses the candidate's basic knowledge of calendars and their ability to apply simple probability concepts.

Updated

Example Answer

Assuming the Gregorian calendar and a year chosen uniformly from a complete 400-year cycle, the probability is 97/400, or 24.25%. A year is a leap year if it is divisible by 4, except century years must also be divisible by 400. There are 100 multiples of 4 in the cycle. We remove the four century years, then restore the one divisible by 400: 100 minus 4 plus 1 equals 97. So 1900 was not a leap year, but 2000 was.

I would state the sampling assumption first. If we choose from a particular short date range, its actual count of leap years determines the probability; 24.25% is not automatically the answer.

Why this works

The explanation matches the calendar rule and keeps the count and denominator in the same 400-year cycle.

Follow-up to prepare for

How would the result change for the Julian calendar, where every fourth year is a leap year?

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