Question

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

• A. $\frac{1}{7}$
• B. $\frac{2}{7}$
• C. $\frac{3}{7}$
• D. $\frac{5}{7}$

Answer 1

The correct option is B $\frac{2}{7}$

A leap year has $52$ full weeks and $2$ other days.
So, the possibilities for the other $2$ days are : (Sun, Mon), (Mon, Tue), (Tue, Wed), (Wed, Thu), (Thu, Fri), (Fri, Sat) and (Sat, Sun)
So, $n\left(S\right)=7$ and $n\left(E\right)=2$
Hence, probability of having $53$ mondays in a leap year is $\frac{2}{7}$