Question

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

• A. $\frac{2}{7}$
• B. $\frac{3}{7}$
• C. $\frac{1}{7}$
• D. $\frac{5}{7}$

Answer 1

The correct option is A $\frac{2}{7}$

Number of days in a leap year = 366
= 7 × 52 + 2
= 52 weeks and 2 days

These 2 day can be
Case (i): Mon and Tue
Case (ii): Tue and Wed
Case (iii): Wed and Thu
Case (iv): Thu and Fri
Case (v): Fri and Sat
Case (vi): Sat and Sun
Case (vii): Sun and Mon

Out of above seven cases, case (v) and case (vi) are the two favorable cases:

$\therefore \text{The required probability}=\frac{2}{7}$