Question

The probability that a leap year, selected at random, contains either 53 Sundays or 53 Mondays, is:

• A. 1/7
• B. 2/7
• C. 3/7
• D. None of these

Hint:

List all 7 possible “extra day” pairs in a leap year and count how many include Sunday or Monday, without double-counting the Sun-Mon pair.

Answer 1

The Correct Option is C

Since only the 2 “extra” days beyond the 52 full weeks can create a 53rd occurrence of any weekday, it helps to just list all 7 equally likely extra-day pairs and mark which ones qualify.

1. The 7 possible pairs: Sun-Mon, Mon-Tue, Tue-Wed, Wed-Thu, Thu-Fri, Fri-Sat, Sat-Sun.
2. Mark the pairs containing Sunday: Sat-Sun and Sun-Mon (2 pairs).
3. Mark the pairs containing Monday: Sun-Mon and Mon-Tue (2 pairs).
4. Counting the Sunday-or-Monday pairs without double-counting Sun-Mon (which satisfies both): Sat-Sun, Sun-Mon, Mon-Tue, a total of 3 distinct pairs out of 7.

So the probability is $\frac{3}{7}$.

The correct answer is option C.