The probability that a leap year selected at random will have 53 Mondays is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(\displaystyle\frac{2}{7}\)
A leap year has 366 days, that is, 52 weeks and 2 days.
The 52 weeks give 52 Mondays. A 53rd Monday occurs only if one of the 2 extra days is a Monday.
The two extra days are consecutive, so they form one of 7 equally likely pairs:
(Sun, Mon), (Mon, Tue), (Tue, Wed), (Wed, Thu),
(Thu, Fri), (Fri, Sat), (Sat, Sun)
Two of these pairs contain a Monday:
\( \displaystyle P(53 \text{ Mondays}) = \frac{2}{7} \)
Tip: For a non-leap year (365 days = 52 weeks and 1 day) the same probability is \(\frac{1}{7}\).