Question

What is the probability that a leap year selected at random will consist of $53$ Sundays?

Answer 1

Determining the probability

The leap year has $366$ days.

The number of full weeks in $366$ days $=52$.

The remaining $2$ days can be any one of the seven weekdays.

So, we have the total number of outcomes $=7$.

and the number of favorable outcomes $=2$.

The formula for probability is

$$\begin{gathered} Probability=\frac{Numberoffavorableoutcomes}{Totalnumberofoutcomes} \\ \therefore P\left(53Sundays\right)=\frac{2}{7} \end{gathered}$$

Therefore, the probability of a leap year consisting of $53$ Sundays is $\frac{2}{7}$.