An inclusive integer interval
The number wheel chooses an integer j from the inclusive range a through b. When a = 1 and b = 10, there are ten outcomes and P(j) = 1/10. Integers are discrete: 4 and 5 are possible, while 4.5 is not part of this model.
A ticket-number example
For tickets numbered 1 to 10, ticket 7 has a 10% pre-draw chance. If 7 wins and the ticket is removed before a second prize, each of the remaining nine tickets has probability 1/9 next. Leaving 7 active would deliberately permit a second win.
Count actual labels
The usual error is setting a range that includes missing or ineligible labels. A range of 1 to 10 is only fair if every number represents one equal item. Numbering ten apartments while one is vacant is not the same experiment as selecting among nine occupied apartments.
What intervals do not model
This tool cannot attach greater likelihood to a number, choose decimal measurements, or create a ranking. Use an explicitly weighted method for unequal tickets and a shuffle for an ordered sequence.
Verify a range by counting
The inclusive count is b minus a plus one. Thus 14 through 18 contains five labels, not four: 14, 15, 16, 17, and 18. This small check catches an endpoint mistake before a raffle or classroom exercise begins. Negative numbers work by the same rule; minus 3 through 7 contains eleven integers. The numeric order matters here in a way it does not for named categories.
Numbers can stand for physical tickets
A school fair may sell tickets 101 through 150. There are 50 eligible integers, because 150 minus 101 plus one equals 50; ticket 127 therefore has a 2% chance. Check that every printed ticket in that interval was actually sold before using the result. If unsold numbers remain, either exclude them or map only sold ticket identifiers into the draw.
Before selecting a label
Write the lowest and highest valid identifiers on the record, then count the endpoints inclusively. This detects a skipped ticket or an accidental extra number before a result has social consequences.
Result record
Save the drawn integer beside the actual ticket or item it represents; a bare number loses its practical meaning.