Question

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

• A. $\frac{1}{7}$
• B. $\frac{2}{7}$
• C. $\frac{3}{7}$
• D. $\frac{4}{7}$

Answer 1

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

We know that a leap year has 366 days and thus a leap year has 52 weeks and 2 days over.

The two left over (successive days have the following likely cases:

(i) Sunday and Monday
(ii) Monday and Tuesday
(iii) Tuesday and Wednesday
(iv) Wednesday and Thursday
(v) Thursday and Friday
(vi) Friday and Saturday
(vii) Saturday and Sunday

$\therefore$ Number of exhaustive cases 'n' = 7

Out of these, the favorable cases are (i) and (vii)

$\therefore$ Number of favorable cases 'm' = 2

$\therefore Probabilityofhaving53Sundays=\frac{2}{7}$