Answer :

P(53 Sundays) = P(Leap Years)P(53 Sundays in a Leap Year) + P(Non-Leap Years)P(53 Sundays in a Non-Leap Year) (1)


Now,


P(53 Sundays in a Leap Year) (52 Weeks + 2 days Saturday + Sunday or Sunday + Monday)


P(53 Sundays in a non-Leap Year) (52 Weeks + 1 day)


Next step in solving this problem requires the total number of leap years in 22nd Century.


Leap Years = 24


Non Leap Years = 76


P(Leap Year)


P(Non-Leap Year)


We now have all the required information, using equation (1) we get





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