Question

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Answer 1

A normal year has 52 Mondays, 52 Tuesdays, 52 Wednesdays, 52 Thursdays, 52 Fridays, 52 Saturdays and 52 Sundays + 1 day that could be anything depending upon the year under consideration. In addition to this, a leap year has an extra day which might be a Monday or Tuesday or Wednesday...or Sunday. 

We've now reduced the question to : what is the probability that in a given pair of consecutive days of the year one of them is a Sunday?

Our sample space is S : {Monday-Tuesday, Tuesday-Wednesday, Wednesday-Thursday,..., Sunday-Monday}
Number of elements in S = n(S) = 7
What we want is a set A (say) that comprises of the elements Saturday-Sunday and Sunday-Monday i.e. A : {Saturday-Sunday, Sunday-Monday}
Number of elements in set A = n(A) = 2
By definition, probability of occurrence of A = n(A)/n(S) = 2/7

Therefore, probability that a leap year has 53 Sundays is 2/7. (Note that this is true for any day of the week, not just Sunday)

Answer 2

Answer:

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.