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Asked by Saksham gaur Last Modified
Answer
Kapil Muni Singh
Engineer
It is a problem of conditional probability. A century have 100 years in which 25 years are leap years(because leap year occurs after every 4 years) and 100-25=75 non-leap years.
For leap year,
The probability of a leap year in a century is 25/100 = 1/4
The probability of getting 53rd sunday in a leap year is 2/7 (A leap year has 52 weeks and 2 days. So, 53rd sunday can occur 2 times out of 7 possibilities, ((sunday,monday), (monday,tuesday), (tuesday,wednesday), (wednesday,thursday), (thursday, friday), (friday,saturday), (saturday,sunday)))
So, the probability of getting 53 sundays in a leap year is (1/4) * (2/7) = 2/28
For non leap year,
The probability of getting a non leap year in a century is 75/100 = 3/4
The probability of getting 53rd sunday in a non leap year is 1/7 (A non leap year has 52 weeks and 1 day. So, sunday can occur 1 time out of 7 possibilities (sunday, monday, tuesday, wednesday, thursday, friday, saturday))
The probability of getting 53 sundays in a non leap year is (3/4) * (1/7) =3/28
Thus, the probability of getting 53 sundays in a century is (2/28) + (3/28) = (5/28)
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