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Question

Find the probability of getting 53 sundays in :
1) a non-leap year
2)leap year

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Solution

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.
Probablity =1/7=0.1428

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.
Probablity=2/7=0.28


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