what is the probability of having 53 Sunday in non leap year
Answers
A non-leap year has 365 days
A year has 52 weeks. Hence there will be 52 Sundays for sure.
52 weeks = 52 x 7 = 364 days .
365– 364 = 1day extra.
In a non-leap year there will be 52 Sundays and 1day will be left.
This 1 day can be Sunday, Monday, Tuesday, Wednesday, Thursday,friday,Saturday, Sunday.
Of these total 7 outcomes, the favourable outcomes are 1.
Hence the probability of getting 53 sundays = 1 / 7. 2) ∴ probability of getting 52 sundays = 1 - 1/ 7 = 6 / 7.
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considering a non leap year
see we have 365 days in a non-leap year.
52 weeks and one extra day= 365 days
52 weeks means definitely there are 52 sundays (this is true for all other days also).
that means if the extra day comes out to be sunday then we will have 53 sundays.
so now the ques boils down to what is the prob of this extra day to be a sunday .
this extra one day can be {monday or tuesday or wednesday or thursday or friday or saturday or sunday }= samplespace (s)
i.e n(s) = 7
so prob of this extra one day to be a sunday is 1/7.
[note - this is also the answer for having 53 mondays or 53 tuesdays or 53 wednesdays or 53 thursdays or 53 fridays or 53 saturdays.]
considering a leap year
leap year contains 366 days
52 weeks plus two two extra days
52 weeks means definitely there are 52 sundays (this is true for all other days also).
if either of these two is sunday then we will have 53 sundays
these two days can be {mon, tue} or { tue , wed} or { wed , thurs} or {thurs , fri} or { fri, sat} or { sat , sun} or {sun , mon} i.e total =7
out of these only two outcomes i.e { sat , sun} and {sun , mon} is having sunday with them .
so our desired prob is 2/7.
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Hello!!
For solving this question we should know a basic fact about a year i.e. it has 52 weeks.
52 weeks means 52×7 = 364 days.
If the year in an ordinary year, the one odd day could be Monday,Tuesday, Wednesday…… Sunday. Thus the probability of getting a sunday is 1/7.
If the year is a leap year, the two odd days could be
Mon Tue, Tue Wed, Wed Thu , Thu Fri , Fri Sat , Sat Sun , Sun Mon.
Thus the probability of getting a sunday is 2/7
Hope this Helps !!
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The probability of a year being a leap year is 14and being non-leap is34
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 27.
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.