What is probability that the 13th day of randomly chosen month is a Friday?

We want the
probability that the 13th day of a randomly chosen month is the 13th.

The
naive answer is 1/7 as it would appear that each date is equally likely to be one of the seven
days of the week.

There are 14 different calendars that we must consider. For
each Jan 1, we consider what happens if it is Mon, Tues, etc... for the rest of the year. This
creates seven different possible calendars. But we must also consider leap years so that creates
seven more.

For non-leap years:

(1)...