Calculate at least one event using the complement
For independent trials with a fixed event probability, subtract the chance of no events from one.
The distinction that matters
If the event probability is p on each of n independent trials, the chance of at least one event is 1 − (1 − p)^n. This answers only whether the named event occurs. It does not establish a profit because the event's payout and the cost of all trials may differ.
A worked example
For a toy event with p = 0.1 across five independent trials, the chance of at least one is 1 − 0.9^5 = 0.40951, about 40.95%. The chance is not 50%: adding five 10% probabilities double-counts sequences with more than one event.
Your next steps
- Define the event precisely.
- Confirm fixed probabilities and independence are justified.
- Use the complement formula with the correct trial count.
- Keep event probability separate from monetary profit.
Where this answer stops
The toy probability is not a real game's hit rate. An RTP percentage cannot be substituted for p. The formula should not be used to choose how long to gamble or to promise that an event will occur.
Sources & reading
Original Northline explanation. Worked examples use stated assumptions; they do not establish an operator’s policy or predict personal results. Read how we handle evidence.
An editorial review date is not a new policy effective date. Always check the current source for operator-specific conditions.
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