What is the probability that a leap year selected at random, will have either 53 Sundays or 53 Saturdays?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(\frac{3}{7}\)
A leap year has 366 days, that is, 52 full weeks and 2 extra days. The 52 weeks give 52 of every weekday; a weekday occurs a 53rd time only if it is one of the two extra days.
The two extra days are two consecutive weekdays, with 7 equally likely pairs:
(Sun, Mon), (Mon, Tue), (Tue, Wed), (Wed, Thu), (Thu, Fri), (Fri, Sat), (Sat, Sun)
Favourable pairs, containing a Sunday or a Saturday:
(Fri, Sat) — 53 Saturdays
(Sat, Sun) — 53 Saturdays and 53 Sundays, counted once
(Sun, Mon) — 53 Sundays
Probability \(\displaystyle =\frac{3}{7}\)
Tip: Adding the two chances, \(\frac{2}{7}+\frac{2}{7}=\frac{4}{7}\) (Option 4), counts the pair (Sat, Sun) twice; for “either … or” the common case is taken once.