Question

What is the probability that a leap year has 53 Sundays?

Answer 1

A leap year has 366 days i.e., 52 weeks and 2 days.

There are 52 Sundays in 52 weeks.

For the remaining 2 days,

Sample space is

S =	{(Mon., Tue.), (Tue., Wed.), (Wed., Thur.),
	(Thur., Fri.), (Fri., Sat.), (Sat., Sun.), (Sun., Mon.)}

∴ n(S) = 7

Let A be the event that the remaining two days are Sundays.

∴ A = {(Sat., Sun.), (Sun., Mon.)}

∴ n(A) = 2

∴ `P(A) = (n(A))/(n(S))`

∴ `P(A) = 2/7`

∴ The probability that a leap year has 53 Sundays is `2/7`.