The probability of not getting 53 Tuesdays in a leap year is:

The correct answer is Option (4) → \(\displaystyle\frac{5}{7}\)

A leap year has 366 days:

    \(366 = 52 \times 7 + 2\)

The 52 complete weeks give 52 Tuesdays. The 2 extra days are two consecutive days, one of 7 equally likely pairs:

    (Mon, Tue), (Tue, Wed), (Wed, Thu), (Thu, Fri), (Fri, Sat), (Sat, Sun), (Sun, Mon)

A 53rd Tuesday comes only from (Mon, Tue) or (Tue, Wed):

    \( \displaystyle P(53 \text{ Tuesdays}) = \frac{2}{7} \)

By the complement rule:

    \( \displaystyle P(\text{not } 53 \text{ Tuesdays}) = 1 - \frac{2}{7} = \frac{5}{7} \)

Tip: \(\frac{2}{7}\), Option (1), is the probability of getting 53 Tuesdays; the question asks for not getting them.