If a leap year is selected at random, what is the chance that it will contain 53 tuesdays?

.: A leap year has 366 days, which contain 52 full weeks + 2 Extra Days.

The extra days can occur as:

(Monday, Tuesday),

(Tuesday, Wednesday),

(Wednesday, Thursday),

(Thursday, Friday),

(Friday, Saturday),

(Saturday, Sunday)

and (Sunday, Monday).

Thus, total no. of exhaustive cases = 7.

Out of these two are favourable i.e.

(Monday, Tuesday) and

(Tuesday, Wednesday)

Required Probability $= \cfrac{2}{7}$