Plz explain probability related to leap years
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Plz explain probability related to leap years
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The probability of a year being a leap year is 1/4 and being non-leap is 3/4.A leap year has 366 days or 52 weeks and 2 odd days. The two odd days can be {Sunday,Monday},{Monday,Tuesday},{Tuesday,Wednesday}, Wednesday,Thursday},{Thursday,Friday},{Friday,Saturday},{Saturday,Sunday}.So there are 7 possibiliyies out of which 2 have a Sunday. So the probability of 53 Sundays in a leap year is 2/7.
A non-leap year has 365 days or 52 weeks and 1 odd day. The odd day can be Sunday,Monday, Tuesday,Wednesday,Thursday,Friday or Saturday.
So there are 7 possibilities out of which 1 is favorable. So the probability of 53 Sundays in non-leap year is 1/7.So the probability of 53 Sundays in a year is 1/4×2/7+3/4×1/7=2/28+3/28=5/28
Note:The probability of a year being leap is normally taken to be 1/4 but more exactly it is 97/400 as out of century years only those divisible by 400 are leap. For example out of 2100,2200,2300,2400 only 2400 is leap.
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