Sum

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

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#### Solution

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`.

Concept: Probability of an Event

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