Question

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

 

Answer 1

We know that a leap year has 366 days (i.e. 7 \[\times\] 52 + 2) = 52 weeks and 2 extra days.
The sample space for these two extra days is given by
S = {(Sunday, Monday), (Monday, Tuesday), (Tuesday, Wednesday), (Wednesday, Thursday), (Thursday, Friday), (Friday, Saturday), (Saturday, Sunday)}
There are 7 cases.
i.e. n(S) = 7
Let E be the event in which the leap year has 53 Sundays and 53 Mondays.
Then E = {(Sunday, Monday) }
i.e. n(E) = 1

\[\therefore P\left( E \right) = \frac{n\left( E \right)}{n\left( S \right)} = \frac{1}{7}\]

Hence, the probability in which a leap year has 53 Sundays and 53 Mondays is \[\frac{1}{7} .\]