Question

Find the probability that a leap year selected randomly will have $53$ Sundays.

Answer 1

A leap year contain $366$ days i.e. $52$ weeks and $2$ days, clearly there are $52$ Sundays in $52$ weeks.

For the remaining two days, we may have any of the two days.

$\left(i\right)$Sunday and Monday,

$\left(ii\right)$ Monday and Tuesday,

$\left(iii\right)$ Tuesday and Wednesday,

$\left(iv\right)$ Wednesday and Thursday,

$\left(v\right)$ Thursday and Friday,

$\left(vi\right)$ Friday and Saturday and

$\left(vii\right)$ Saturday and Sunday.

Now for $53$ Sundays, one of the two days must be Sundays, hence required probability $=\frac{2}{7}$