Q.What is the chance that a leap year, selected at random, will contain 53 Sundays?

A leap year has 366 days $=52\times7+2$, so it always contains 52 complete weeks (hence 52 Sundays for sure) plus 2 extra days. Those 2 extra days can be any of the 7 equally likely consecutive pairs: (Sun,Mon), (Mon,Tue), (Tue,Wed), (Wed,Thu), (Thu,Fri), (Fri,Sat), (Sat,Sun). A 53rd Sunday occurs exactly when Sunday i …

Reduce the 366-day year to 52 full weeks plus 2 'extra' days, then find how many of the 7 equall …

Using 365 days (an ordinary, non-leap year) instead of 366, which changes the extra-day cou …