Rare events become likely with enough attempts. A 1% chance per try gives about a 63% chance over 100 tries.
How to use the Probability of At Least One Calculator
- Probability per try
- Number of tries
- Want to work backwards? Type a value into At least once and Number of tries is calculated for you.
Results update as you type, and every field accepts the units shown in its menu.
How it works
Find the chance of the event never happening and subtract it from one.
Inputs explained
| Field | What to enter |
|---|---|
| Probability per try | In % |
| Number of tries | A number |
What each result means
- At least once = (1 – (1 – [Probability per try]÷100)^[Number of tries])×100
- Tries for 50% chance = ceil(ln(0.5)÷ln(1 – [Probability per try]÷100))
- Tries for 95% chance = ceil(ln(0.05)÷ln(1 – [Probability per try]÷100))
Example values
How the main result changes when Number of tries changes and everything else stays at the example values above:
| Number of tries | At least once (%) |
|---|---|
| 50 | 39.499 |
| 75 | 52.941 |
| 100 | 63.397 |
| 125 | 71.529 |
| 150 | 77.855 |
| 200 | 86.602 |
Formula
P(at least one) = 1 − (1 − p)ⁿWorked example
Inputs — Probability per try: 1 %; Number of tries: 100.
Results — At least once = 63.397 %; Tries for 50% chance = 69; Tries for 95% chance = 299.
Frequently asked questions
Is this the drop-chance formula used in games?
Yes, assuming each try is independent.
Why is it not simply n × p?
That overcounts overlapping successes and can exceed 100%.
What formula does the Probability of At Least One Calculator use?
P(at least one) = 1 − (1 − p)ⁿ.
Can I work backwards from the result?
Yes. Type the result you want into At least once and the calculator finds the matching number of tries.