Random Number Between 1 and 5
The box above gives a whole number from 1 to 5, each one time in five. It draws on load and again on the button, and keeps no memory of what it showed before.
1 to 5 1
5 possible values, each equally likely. Tick nothing and repeats can happen; that is what random means.
The odds
Five outcomes, 20 per cent each, one chance in five. Both ends included.
The die trick that fails
Rolling a d6 and folding the 6 back onto 1 looks reasonable and is not. It gives 1 two faces out of six, a 33.3 per cent chance, while 2, 3, 4 and 5 get 16.7 per cent each. Reroll the 6 instead: that is fair, it just occasionally costs a second roll. A d10 halved is exact, with 1 and 2 as one, 3 and 4 as two, and so on to 9 and 10 as five. A d20 read in fours works the same way.
Seeing all five takes longer than five draws
Five draws produce five different numbers only 3.84 per cent of the time. On average it takes 11.4 draws before every value has appeared at least once, and even after ten draws there is a 47.7 per cent chance that one of the five is still missing. Missing values are the normal state of a short run, not a fault.
What it is for
Star ratings, five-way choices, picking a row out of five, or an unbiased answer on a 1 to 5 scale when you are testing a form. Neighbouring ranges are 1 to 4, 1 to 6 and 1 to 10. Anything else is on the random number generator.