Find the probability that there are 53 Sundays in a randomly chosen leap year.

The probability that there are 53 Sundays in a randomly chosen leap year is 

(A) $\dfrac{1}{7}$ 

(B) $\dfrac{1}{14}$ 

(C) $\dfrac{1}{28}$ 

(D) $\dfrac{2}{7}$ 

(GATE 2005) 

Answer: (D) $\dfrac{2}{7}$ 

Explanation: 

A leap year has 366 days. 

Since, $\dfrac{364}{7} = 52$, there will 52 Sunday in 364 days. The remaining 2 days can be any of the following: 

$\{(Sunday, Monday), (Monday, Tuesday), (Tuesday, Wednesday), \\(Wednesday, Thursday), (Thursday, Friday), (Friday, Saturday), \\(Saturday, Sunday)\}.$ 

Therefore, the required probability is $\dfrac{2}{7}$.