What is the probability that a leap year has 52 Mondays?

Question:

What is the probability that a leap year has 52 Mondays?

(a) $\frac{2}{7}$

(b) $\frac{4}{7}$

(c) $\frac{5}{7}$

(d) $\frac{6}{7}$

 

Solution:

GIVEN: A leap year

TO FIND: Probability that a leap year has 52 Mondays.

Total number of days in leap year is 366days

Hence number of weeks in a leap year is 

In a 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 52 Mondays the additional days should not include Monday

Hence total number of pairs of days is 7

Favorable day i.e. in which Mondays is not there is 5

We know that PROBABILITY = 

Hence probability that a leap year has 52 Mondays is equal to

Hence the correct option is

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