Question

What is the probability that a leap year selected will contain $53$ sundays?

Answer 1

Number of days in a leap year $=366days$
$366days=52$ weeks and $2$ days
The remaining $2days$ can be
(i) Sunday and Monday
(ii) Monday and Tuesday
(iii) Tuesday and Wednesday
(iv) Wednesday and thursday
(v) Thursday and Friday
(vi) Friday and Saturday
(vii) Saturday and Sunday.
For the leap year to contain $53$ sundays, last two days are either Sunday and Monday or Saturday and Sunday.
Number of such favourable outcomes $=n\left(A\right)=2$
Total possible outcomes in sample space $=n\left(S\right)=7$
$\therefore P\left(A\right)=\frac{n\left(A\right)}{n\left(S\right)}\therefore P_{\left(\text{a leap year contains}53sundays\right)}=\frac{2}{7}$