Question

If the first day of an ordinary year is Thursday, then probability that the last day of the year is Thursday will be

Answer 1

Answer:

Within any year, 1-Jan and 31-Dec will be the same day of the week, UNLESS it its a leap year. (For example, 2018 began and ended on a Monday.) This is because 365 = 1 (mod 7.)

So really your question is identical to "what is the probability that this is not a leap year?" Under the current calendar, there are 97 leap years out of every 400, so the probability that this is NOT leap year, and thus the probability that the year starts and ends on the same day of the week, is 303/400.