Draws
Bingo Probability Calculator
Calculate a specified bingo pattern or any completed line on a standard 75-ball card by a chosen call count, using draws without replacement.
Your result
0.82567229%
Chance specified pattern is complete
- Required distinct numbers
- 5
- Balls called
- 30
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One specified pattern; excludes any-line union and the chance of beating other players.
Probability of a specified bingo line
If r distinct required numbers must appear in d draws from an N-number pool, the probability is C(d,r) / C(N,r). With 75 numbers, five required numbers and 30 calls, this is C(30,5)/C(75,5), about 0.82567%.
If a free center is part of that particular five-square line, only four numbered squares need to be drawn. Enter four, not five. The tool assumes uniform draws without replacement and one fixed known pattern.
A specified line is different from winning the game
Any-line mode models one standard 5×5 card with a free center and 24 distinct numbers in a 75-ball pool. It counts all five rows, five columns and two diagonals using inclusion–exclusion across overlapping patterns. Multiplying by 12 would double-count cards with several complete lines.
The card’s printed numbers do not change that one-card probability under a uniform 75-ball draw, as long as its 24 numbered squares are distinct. Other shapes, duplicate square numbers or different winning patterns need their own layout. Competing-player winning chances also depend on their cards.
For a generic independent repeated event use the probability calculator; a bingo ball draw is not an independent-trial model.