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