Probability Calculator guide
Probability Calculator: Two Events and Repeated Trials
Use our probability calculator to work out the chance of A and B, A or B, neither, and an event happening at least once over several tries.
By the AllCalculator editorial teamUpdated 16 October 20261 min read
Probability measures how likely something is, from 0% (impossible) to 100% (certain). Our Probability Calculator combines two independent events and works out repeated tries.
How to use the calculator (Probability Calculator)
- Enter the probability of A and the probability of B as percentages.
- Enter a number of tries to see repeated-event results.
The rules
For independent events (one doesn't affect the other):
| Result | Formula |
|---|---|
| A and B | P(A) × P(B) |
| A or B (or both) | P(A) + P(B) − P(A) × P(B) |
| Not A | 1 − P(A) |
| Neither | (1 − P(A)) × (1 − P(B)) |
| A at least once in n tries | 1 − (1 − P(A))ⁿ |
A worked example
With the calculator's default settings, P(A) = 50% and P(B) = 30%:
- Both: 0.5 × 0.3 = 15%
- Either: 0.5 + 0.3 − 0.15 = 65%
- Neither: 0.5 × 0.7 = 35%
- A at least once in 5 tries: 1 − 0.5⁵ = 96.9%
Frequently asked questions
What does independent mean?
That one event doesn't change the chance of the other, like two coin tosses. Drawing two cards without putting the first back isn't independent.
What's the difference between probability and odds?
A probability of 25% means odds of 1 to 3 (one success for every three failures), or 3 to 1 against.
Does a coin "owe" me heads after several tails?
No. Each toss is independent, so the chance is still 50%. That mistake is called the gambler's fallacy.
For counting outcomes, use our Permutation and Combination Calculator.
Sources and further reading
- GOV.UK: National curriculum in England – mathematicsgov.uk
- Wolfram MathWorld: Probabilitymathworld.wolfram.com
Links open official and independent websites in a new tab.
This guide is general information to help you understand your options. It isn't financial, tax, legal or building advice and doesn't take your personal circumstances into account. Figures were checked when the guide was last updated and can change, so confirm anything important with GOV.UK, HMRC, a regulated adviser or a qualified tradesperson.