Question

what is the probability of having 53 Sunday's in a leap year

Answer 1

In a leap year, total days = 366.

So there will be total 52 weeks and 2 days.

52 weeks will have 52 Sundays.

The last two days can be one of the following 7 possibilities:
Monday and Tuesday
Tuesday and Wednesday
Wednesday and Thursday
Thursday and Friday
Friday and Saturday
Saturday and Sunday
Sunday and Monday

Number of times of having 53rd sunday = 2 (Saturday and Sunday AND. Sunday and Monday)

So total possibilities = 7

favourable possibilities(of having 53 Sundays) = 2

Thus Probability of having 53 Sundays = 2/7

Answer 2

here is your answer

OK

see answer

best answer here.........


here in ques it is not specifically said that the year is leap year or non leap year . so i am writing the answer for both conditions.

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.


hope it help you