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

We know that, in a leap year there are total 366 days, 52 weeks and 2 days

Now, in 52 weeks there are total 52 Tuesdays

∴ Probability that the leap year will contain 53 Tuesdays is equal to the probability of remaining 2 days will be Tuesdays

Thus, the remaining two days can be:

(Monday and Tuesday), (Tuesday and Wednesday), (Wednesday and Thursday), (Thursday and Friday), (Friday and Saturday), (Saturday and Sunday) and (Sunday and Monday)

∴ Total Number of cases = 7

Cases in which Tuesday can come = 2

Hence, probability (leap year having 53 Tuesdays)