What is the probability that an year will have 53 Tuesdays
That depends on the leap years.
e.g
number of Tuesdays in our leap-year cycle:
2016 -- 52
2017 -- 52
2018 -- 52
2019 -- 53
So in any leap-year cycle there are 3(52) + 53 or 209 Tuesdays
and in that leap-year cycle there are 3(365) + 366 or 1460 days
(ignoring the fact that every 100 years, the leap year is skipped and every 400 years it is put back in: Zeller's congruence .... )
prob(of your event) = 209/1460 = appr .14315