How to use the probability calculator
- 1 Enter the probability of event A as a percentage.
- 2 Enter the probability of event B.
- 3 Enter the number of trials for the repeated-event results.
- 4 Read P(A and B), P(A or B), neither, and the chances over several trials.
Worked example
Two independent events with P(A) = 50% and P(B) = 40%. Both happen with probability 0.5 × 0.4 = 20% (1 in 5). At least one happens with 50% + 40% − 20% = 70%, and neither with 30%. Over 3 trials, A happens at least once with 87.5% probability.
Thinking clearly about chance
- Check independence: one event must not change the other.
- Multiply for and, add and subtract for or.
- Use the complement for at least once problems.
- Convert to odds to make small chances easier to picture.
Standardize scores with the Z-Score Calculator, build intervals with the Confidence Interval Calculator, and express results with the Percentage Calculator. Add fractional chances with the Mixed Number Calculator.
How it works: The rules used are the multiplication rule for independent events and the addition rule with the overlap taken away once. For repeated trials, it is easier to work out the chance of never succeeding, (1 − p) to the power n, and subtract that from one.
Features
And, or, not
Every combination of two independent events.
Repeated trials
At least once, every time and never, over n tries.
Odds too
The main answer as 1 in N odds.
When to use it
Statistics homework
Check independent event problems. Standardize values with the Z-Score Calculator.
Games and dice
The chance of rolling a six at least once in three throws. Roll real dice with the Dice Roller.
Risk
The chance two independent systems both fail.
Choosing groups
Count arrangements with the Permutation and Combination Calculator.
Related Math tasks
Frequently asked questions
How do you calculate the probability of A and B?
For independent events, multiply: P(A and B) = P(A) × P(B). With 50% and 40%, that is 0.5 × 0.4 = 0.2, or 20%.
How do you calculate the probability of A or B?
P(A or B) = P(A) + P(B) − P(A and B). With 50% and 40%: 0.5 + 0.4 − 0.2 = 0.7, or 70%.
What does independent mean?
One event does not change the probability of the other, like two coin tosses. If events affect each other, you need conditional probability.
What is the probability of neither event?
(1 − P(A)) × (1 − P(B)) for independent events: 0.5 × 0.6 = 30% in the example.
How do I find the chance of something happening at least once?
1 − (1 − p)^n, where p is the chance each time and n is the number of tries. A 50% event happens at least once in 3 tries with 87.5% probability.
What is the chance of rolling a six at least once in four rolls?
1 − (5/6)^4 ≈ 51.8%. Enter 16.667% for A and 4 trials.
What is the difference between probability and odds?
Probability is favorable outcomes ÷ all outcomes. Odds compare favorable to unfavorable. A 20% probability is 1 in 5, or odds of 1 to 4.
What are mutually exclusive events?
Events that cannot both happen, like rolling a 1 and a 2 on one die. Then P(A and B) = 0 and P(A or B) = P(A) + P(B). This calculator assumes independent events instead.
Can probability be more than 100%?
No. Probabilities range from 0 (impossible) to 1 or 100% (certain).
What is a complement?
The probability an event does not happen: 1 − P(A).
How do I convert a percentage to a probability?
Divide by 100. 40% is a probability of 0.4.
What is the probability of flipping heads twice?
0.5 × 0.5 = 0.25, or 25%. Enter 50% for A and 50% for B.
What is the gambler's fallacy?
Believing that past results change the chance of independent events. After five heads, the next flip is still 50% heads.
Built and reviewed by Hamza Farooq, founder and lead developer
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