Find the probability that a leap year has 52 Sundays.

Solution

A leap year can have 52 Sundays or 53 Sundays. In a leap year, there are 366 days out of which there are 52 complete weeks & remaining 2 days. Now, these two days can be (Sat, Sun) (Sun, Mon) (Mon, Tue) (Tue, Wed) (Wed, Thur) (Thur, Friday) (Friday, Sat).
So there are total 7 cases out of which (Sat, Sun) (Sun, Mon) are two favorable cases. So, P (53 Sundays) = 2 / 7
Now, P(52 Sundays) + P(53 Sundays) = 1
So, P (52 Sundays) = 1 – P(53 Sundays) = 1 – (2/7) = (5/7)