**Question:**

What is the probability that a leap year has 53 Tuesdays and 53 Mondays?

**Solution:**

GIVEN: A leap year

TO FIND: Probability that a leap year has 53 Tuesdays and 53 Mondays

Total number of days in a non leap year is 366days

Hence number of weeks in a non leap year is

In a non leap year we have 52 complete weeks and 2 day which can be any pair of the day of the week i.e.

(SUNDAY, MONDAY)

(MONDAY, TUESDAY)

(TUESDAY, WEDNESDAY)

(WEDNESDAY, THURSDAY)

(THURSDAY FRIDAY)

(FRIDAY, SATURDAY)

SATURDAY, SUNDAY)

To make 53 Tuesdays and 53 Mondays the additional days should include Monday and Tuesday

Hence total number of pairs of days is 7

Favorable day i.e. in which one Tuesday and one Monday is there is only 1

We know that PROBABILITY =

Hence probability that a leap year has 53 Tuesdays and 53 Mondays is equal to