Question

Find the probability that a leap year, selected at random, will contain 53 Sundays.

Answer 1

A leap year has 366 days, therefore 52 weeks i.e. 52 Sunday and 2 days. The remaining 2 days may be any of the following:

Sunday and Monday
Monday and Tuesday
Tuesday and Wednesday
Wednesday and Thursday
Thursday and Friday
Friday and Saturday
Saturday and Sunday

For having $53$ Sundays in a year, one of the remaining $2$ days must be a Sunday.

Let $E$ be an event of getting $53$ Sundays

$n\left(S\right)=7,n\left(E\right)=2$

Then, $P\left(E\right)=\frac{n\left(E\right)}{n\left(S\right)}=\frac{2}{7}$