What is the probability of Wednesday falling before Tuesday
in a week?
Answers
Answer:
There are two ways to answer that.
Assuming that January can start on any day of the week with equal probability, just note that for it to have 5 Sundays it has to start on either a Sunday, a Saturday or a Friday, so 3/7. Done.
If you want to be a little more picky with details, you may know that under the Gregorian Calendar that is used in most of the Western World, the same weekdays repeat exactly on the same calendar days every 400 years (so, for example, since 2019 started on a Tuesday, so will 2419, 2819 and so on). Since 400 is not a multiple of seven, it turns out that if you pick any given year (let’s say, since 1583, the first full year after the Gregorian Calendar was promulgated, at least in the Catholic states of Europe at the time), the probabibily of said year beginning with, say, a Monday, or a Tuesday is not exactly 1/7 (though somewhat close). So you’d have to figure out how many years out of 400 start on each of Friday, Saturday or Sunday.
For your benefit, I just did a quick Python program to compute this.
It turns out that over 400 years, January 1 will fall on:
Monday or Saturday, 56 times each
Wednesday or Thursday, 57 times each
Sunday, Tuesday, or Friday, 58 times each
(pretty evenly distributed).
Calculating the referred probability this way will yield 172/400 or 43/100 - a tad above the 3/7 obtained before, but not by much (43% vs 42.857%)
Answer:
0 because the days are defined and can't be changed!