Friday the 13th – Again?

Probabilities of daysDid you know that “Friday the 13th” occurs very frequently? In fact, it is the most common combination of the day-of-the-week and day-of-the-month on our modern-day Gregorian calendar! However, one can say the same for any one of 28 combinations that are equally “most” likely to occur, such as “Sunday the 1st”, “Monday the 2nd”, “Tuesday the 3rd”, “Wednesday the 4th”, and so on. It turns out that all of these common 28 combinations occur in the same month that we find a “Friday the 13th”.

The table below shows the probabilities of all the day-of-the-week and day-of-the-month combinations. Given the fact that the Gregorian calendar repeats every 400 years, it is relatively easy to calculate the statistics (if you’re curious, have a look at the attached C# code).

For those who are superstitious about “Friday the 13th” being filled with doom and gloom, it may be more fortunate to instead think of that entire month as a very-most-special month, considering the fact that the same month contains all of the 28 “luckiest” combinations. Furthermore, in number theory, both the numbers 7 and 13 happen to be a “lucky prime” – that is, a number that is both a prime number and a lucky number. So, the number 13 is really not an unlucky number after all. And besides, Friday is as close as you get to a wonderful weekend!

But if you are set on finding a truly unlucky day, “Wednesday the 31st” might be your day. After all, the day is the one-and-only very-least-likely combination of the day-of-the-week and day-of-the-month to occur, plus Wednesday is as far as you get away from a happy weekend, and the number 31 happens to be 13 in reverse.

Remember, next time a month starts on a Sunday, you are in for a treat: You can pick from “Sunday the 1st”, “Saturday the 7th”, “Friday the 13th” or “Saturday the 28th” (because the number 28 can be interpreted as “double prosperity” in Chinese culture). Or just pick your favorite number from 1 to 28, because that will be your beloved frequently-lucky day-of-the-week!

Day of Month Day of Week Probability (%)
1 Sunday 0.47092001
8 Sunday 0.47092001
15 Sunday 0.47092001
22 Sunday 0.47092001
2 Monday 0.47092001
9 Monday 0.47092001
16 Monday 0.47092001
23 Monday 0.47092001
3 Tuesday 0.47092001
10 Tuesday 0.47092001
17 Tuesday 0.47092001
24 Tuesday 0.47092001
4 Wednesday 0.47092001
11 Wednesday 0.47092001
18 Wednesday 0.47092001
25 Wednesday 0.47092001
5 Thursday 0.47092001
12 Thursday 0.47092001
19 Thursday 0.47092001
26 Thursday 0.47092001
6 Friday 0.47092001
13 Friday 0.47092001
20 Friday 0.47092001
27 Friday 0.47092001
7 Saturday 0.47092001
14 Saturday 0.47092001
21 Saturday 0.47092001
28 Saturday 0.47092001
3 Sunday 0.47023553
6 Sunday 0.47023553
10 Sunday 0.47023553
13 Sunday 0.47023553
17 Sunday 0.47023553
20 Sunday 0.47023553
24 Sunday 0.47023553
27 Sunday 0.47023553
4 Monday 0.47023553
7 Monday 0.47023553
11 Monday 0.47023553
14 Monday 0.47023553
18 Monday 0.47023553
21 Monday 0.47023553
25 Monday 0.47023553
28 Monday 0.47023553
1 Tuesday 0.47023553
5 Tuesday 0.47023553
8 Tuesday 0.47023553
12 Tuesday 0.47023553
15 Tuesday 0.47023553
19 Tuesday 0.47023553
22 Tuesday 0.47023553
26 Tuesday 0.47023553
2 Wednesday 0.47023553
6 Wednesday 0.47023553
9 Wednesday 0.47023553
13 Wednesday 0.47023553
16 Wednesday 0.47023553
20 Wednesday 0.47023553
23 Wednesday 0.47023553
27 Wednesday 0.47023553
3 Thursday 0.47023553
7 Thursday 0.47023553
10 Thursday 0.47023553
14 Thursday 0.47023553
17 Thursday 0.47023553
21 Thursday 0.47023553
24 Thursday 0.47023553
28 Thursday 0.47023553
1 Friday 0.47023553
4 Friday 0.47023553
8 Friday 0.47023553
11 Friday 0.47023553
15 Friday 0.47023553
18 Friday 0.47023553
22 Friday 0.47023553
25 Friday 0.47023553
2 Saturday 0.47023553
5 Saturday 0.47023553
9 Saturday 0.47023553
12 Saturday 0.47023553
16 Saturday 0.47023553
19 Saturday 0.47023553
23 Saturday 0.47023553
26 Saturday 0.47023553
4 Sunday 0.46886657
5 Sunday 0.46886657
11 Sunday 0.46886657
12 Sunday 0.46886657
18 Sunday 0.46886657
19 Sunday 0.46886657
25 Sunday 0.46886657
26 Sunday 0.46886657
5 Monday 0.46886657
6 Monday 0.46886657
12 Monday 0.46886657
13 Monday 0.46886657
19 Monday 0.46886657
20 Monday 0.46886657
26 Monday 0.46886657
27 Monday 0.46886657
6 Tuesday 0.46886657
7 Tuesday 0.46886657
13 Tuesday 0.46886657
14 Tuesday 0.46886657
20 Tuesday 0.46886657
21 Tuesday 0.46886657
27 Tuesday 0.46886657
28 Tuesday 0.46886657
1 Wednesday 0.46886657
7 Wednesday 0.46886657
8 Wednesday 0.46886657
14 Wednesday 0.46886657
15 Wednesday 0.46886657
21 Wednesday 0.46886657
22 Wednesday 0.46886657
28 Wednesday 0.46886657
1 Thursday 0.46886657
2 Thursday 0.46886657
8 Thursday 0.46886657
9 Thursday 0.46886657
15 Thursday 0.46886657
16 Thursday 0.46886657
22 Thursday 0.46886657
23 Thursday 0.46886657
2 Friday 0.46886657
3 Friday 0.46886657
9 Friday 0.46886657
10 Friday 0.46886657
16 Friday 0.46886657
17 Friday 0.46886657
23 Friday 0.46886657
24 Friday 0.46886657
3 Saturday 0.46886657
4 Saturday 0.46886657
10 Saturday 0.46886657
11 Saturday 0.46886657
17 Saturday 0.46886657
18 Saturday 0.46886657
24 Saturday 0.46886657
25 Saturday 0.46886657
2 Sunday 0.46818210
7 Sunday 0.46818210
9 Sunday 0.46818210
14 Sunday 0.46818210
16 Sunday 0.46818210
21 Sunday 0.46818210
23 Sunday 0.46818210
28 Sunday 0.46818210
1 Monday 0.46818210
3 Monday 0.46818210
8 Monday 0.46818210
10 Monday 0.46818210
15 Monday 0.46818210
17 Monday 0.46818210
22 Monday 0.46818210
24 Monday 0.46818210
2 Tuesday 0.46818210
4 Tuesday 0.46818210
9 Tuesday 0.46818210
11 Tuesday 0.46818210
16 Tuesday 0.46818210
18 Tuesday 0.46818210
23 Tuesday 0.46818210
25 Tuesday 0.46818210
3 Wednesday 0.46818210
5 Wednesday 0.46818210
10 Wednesday 0.46818210
12 Wednesday 0.46818210
17 Wednesday 0.46818210
19 Wednesday 0.46818210
24 Wednesday 0.46818210
26 Wednesday 0.46818210
4 Thursday 0.46818210
6 Thursday 0.46818210
11 Thursday 0.46818210
13 Thursday 0.46818210
18 Thursday 0.46818210
20 Thursday 0.46818210
25 Thursday 0.46818210
27 Thursday 0.46818210
5 Friday 0.46818210
7 Friday 0.46818210
12 Friday 0.46818210
14 Friday 0.46818210
19 Friday 0.46818210
21 Friday 0.46818210
26 Friday 0.46818210
28 Friday 0.46818210
1 Saturday 0.46818210
6 Saturday 0.46818210
8 Saturday 0.46818210
13 Saturday 0.46818210
15 Saturday 0.46818210
20 Saturday 0.46818210
22 Saturday 0.46818210
27 Saturday 0.46818210
29 Sunday 0.44080303
29 Tuesday 0.44080303
29 Friday 0.44011855
29 Wednesday 0.43943407
29 Thursday 0.43943407
29 Monday 0.43874960
29 Saturday 0.43874960
30 Monday 0.43190483
30 Wednesday 0.43190483
30 Friday 0.43053588
30 Saturday 0.43053588
30 Sunday 0.42916692
30 Thursday 0.42916692
30 Tuesday 0.42848245
31 Thursday 0.27515965
31 Tuesday 0.27447518
31 Saturday 0.27447518
31 Sunday 0.27379070
31 Monday 0.27310622
31 Friday 0.27310622
31 Wednesday 0.27242175

Attribution: This post’s associated image is an adaption of “Mysterious Attainment”, published under the Creative Commons Attribution 2.0 Generic license, by Joel Penner (FeatheredTar), who is also from Winnipeg.