If a leap-year is selected at random, then what is the chance it will contain 53 Sunday?

A leap-year has 366 days i.e., 52 complete. week and two days more. These two days will be two consecutive days of a week. A leap-year will have 53 Sundays, if out of the two consecutive days of a week selected at random one is a Sunday.

 Let be the sample space and E be the event that out of the two consecutive days of 

a week one is Sunday, then 

S = {(Sunday, Monday), (Monday, Tuesday), (Tuesday, Wednesday), (Wednesday. Thursday), (Thursday, Friday), (Friday   Saturday), (Saturday, Sunday)}; n(S) =7 and E = {(Sunday, Monday), (Friday, Saturday)} 

$\therefore n\left(E\right)=2$

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