Probability of Christmas on Wednesday

Thu, 14 Oct 2021 00:00:00 +0000

Original Problem

Proof: In the system of the current Common Era, the probability of Christmas on Wed. is not 1/7.

What exactly the probability is

In 400 years there are 303 non-leap years and 97 leap years. Total number of days:

$$T = 303\cdot 365 + 97\cdot 366\equiv 303 + 97\cdot 2\equiv 0\pmod 7.$$

This means: If the Christmas is on Mon. in year x, then it would be on Mon. in year (x + 400). That’s to say, there’s a difference between a day of the week and another day of the week.

Mathematica on CuSO4_Deposit

Probability of Christmas on Wednesday

Original Problem

What exactly the probability is