Problem D

A Big Leap

Most people think of a year as \(365\) days, however it is actually slightly more than \(365\) days. To account for this extra time we use leap years, which are years containing one extra day.

Mara uses the flowchart shown to determine whether or not a given year is a leap year. She has concluded the following:

\(2018\) was

**not**a leap year because \(2018\) is not divisible by \(4\).\(2016\) was a leap year because \(2016\) is divisible by \(4\), but not \(100\).

\(2100\) will

**not**be a leap year because \(2100\) is divisible by \(4\) and \(100\), but not \(400\).\(2000\) was a leap year because \(2000\) is divisible by \(4\), \(100\), and \(400\).

If Mara chooses a year greater than \(2000\) at random, what is the probability that she chooses a leap year?