Random Number Between 1 and 31
Thirty-one outcomes, each with a 3.23 percent chance. It is the day-of-the-month range, though a real calendar does not hand out the thirty-first anywhere near that often.
1 to 31 1
31 possible values, each equally likely. Tick nothing and repeats can happen; that is what random means.
3.23 percent each, flat
Every value from 1 to 31 has a 1 in 31 chance, which is 3.23 percent. The tool treats all thirty-one days as equally likely, and that is the right behaviour for a number generator. It is the wrong model of a calendar.
A calendar is not flat
Only seven of the twelve months have a 31st: January, March, May, July, August, October and December. In an ordinary 365-day year there are seven days that are the 31st and twelve days that are the 1st. So if you pick a random day of the year, the 31st turns up 1.92 percent of the time and the 1st turns up 3.29 percent, while this page gives both 3.23 percent. A random day of the month and a random day of the year are two different things, and the 31st is about 1.7 times more likely here than it is in a real year.
What to do with an impossible date
If you drew 31 for a thirty-day month, draw again rather than rounding down to 30. Rounding gives 30 a double share, 6.45 percent instead of 3.23 percent. For a thirty-day month use 1 to 30 in the first place, and pick the month itself with 1 to 12.
Repeats
Two draws in a row match 3.23 percent of the time, but across seven draws the chance that two of them match is 51.83 percent. Seeing all thirty-one values takes about 125 draws on average.
Uses
- Picking a date for something you do not mind the timing of
- A daily prompt from a list of thirty-one
- Any thirty-one-item list, drawn with the main generator if you want a different range