Loading calculator...
- Combines two independent events: and, or, exactly one, neither.
- Finds the probability and odds of a single event from outcomes.
- Works out the chance of at least one success in n tries.
- Shows every formula used.
How to use the probability calculator
Choose a mode
Two events, a single event, or at least once in n tries.
Enter the probabilities
Use decimals from 0 to 1, such as 0.4 for 40%.
Or enter outcomes
For a single event, type favorable and total outcomes.
Read the results
All the related probabilities appear together with the working.
Probability rules
Two independent events
P(A and B) = P(A) × P(B)
P(A or B) = P(A) + P(B) − P(A and B)
P(neither) = 1 − P(A or B)
Independent means one event does not change the chance of the other, like two coin flips.
Single event and repeated tries
P(event) = favorable outcomes ÷ total outcomes
P(at least once in n tries) = 1 − (1 − p)ⁿ
Example 1: two events
P(A) = 0.5, P(B) = 0.4.
- P(A and B) 0.2
- P(A or B) 0.7
- P(exactly one) 0.5
- P(neither) 0.3
Exactly one is the “or” result minus the chance of both.
Example 2: a single event
3 favorable outcomes out of 10.
- Probability 30%
- Odds for 3 : 7
- Odds against 7 : 3
Example 3: at least once
A 10% chance each try, 10 tries.
- At least once 65.1322%
- Never 34.8678%
- Tries for a 50% chance 7
Rolling at least one six in 4 rolls of a die has a 51.7747% chance.
Where a probability calculator helps
Math and statistics
Check and/or rules and complement problems.
Games and dice
Work out the chance of rolls, draws and wins.
Risk and reliability
See the chance that at least one of several parts fails.
Everyday odds
Turn outcome counts into percentages and odds.
Count outcomes with the permutation and combination calculator, find the chance of exactly k successes with the binomial distribution calculator, or use the normal curve with the z-score calculator.
Probability calculator FAQ
How do you calculate probability?
Divide the number of favorable outcomes by the total number of equally likely outcomes.
How do I find the probability of A and B?
For independent events, multiply: P(A) × P(B).
How do I find the probability of A or B?
Add the two probabilities and subtract the chance of both: P(A) + P(B) − P(A and B).
What is the probability of at least one?
Work out the chance of none, then subtract from 1: 1 − (1 − p)ⁿ.
What is the difference between probability and odds?
Probability compares favorable outcomes to all outcomes. Odds compare favorable to unfavorable. A 30% chance is odds of 3 to 7.
What if my events are not independent?
These formulas assume independence. For dependent events, you need the conditional probability of one given the other.