What past draws can—and cannot—tell you

Start with the assumptions

If draws are fair and independent, a number being frequent or absent in past draws does not change its probability in the next draw. A frequency chart describes the sample you selected; it does not establish predictive advantage.

A small example

For a fair six-sided die, the probability of a six on the next roll is 1/6, even after five rolls without a six. Independence is the key assumption. This is a teaching example, not an audit of any lottery.

Read a chart carefully

Check the source, sample size, date range, rules and treatment of special numbers. Investigate missing or duplicate records before interpreting a pattern. QuantPath labels the official source and retrieval time of its draw history. Demo model results remain synthetic.

Further reading

• OpenStax · Independent and mutually exclusive events