Question

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

Answer 1

Since in a leap year, there are $52$ weeks and two days.
Now, we need to find the probability of these extra two days.
The sample space for the two extra days will be $S=$$\left\{\right(M,T),(T,W),(W,TH),(TH,F),(F,S),(S,SU),(SU,M\left)\right\}$

$\therefore n\left(S\right)=7$

Event of getting Sunday and Monday is $E=\{SU,M\}$

$\Rightarrow n\left(E\right)=1$
Thus, $P\left(E\right)=\frac{n\left(E\right)}{n\left(S\right)}$

$\therefore P\left(E\right)=\frac{1}{7}$