Probability Calculator
Calculate the probability of events, unions, intersections, normal distributions, and more.
Modify the values and click Calculate to get instant results.
Modify the values and click Calculate to get instant results.
Probability of Two Events
Find union, intersection, and related probabilities of two independent events.
Probability of A: P(A)
Probability of B: P(B)
Please input values between 0 and 1.
Result
| P(A′) — A NOT occurring | |
| P(B′) — B NOT occurring | |
| P(A∩B) — Both A and B occur | |
| P(A∪B) — A or B or both occur | |
| P(A▵B) — A or B but NOT both | |
| P((A∪B)′) — Neither A nor B |
Probability Solver for Two Events
Provide any 2 values below to calculate the rest (independent events).
P(A)
P(B)
P(A′) — A NOT occurring
P(B′) — B NOT occurring
P(A∩B) — Both occur
P(A∪B) — A or B or both
P(A▵B) — A or B, not both
P((A∪B)′) — Neither
Please input values between 0 and 1.
Result
| P(A) | |
| P(B) | |
| P(A′) | |
| P(B′) | |
| P(A∩B) | |
| P(A∪B) | |
| P(A▵B) | |
| P((A∪B)′) |
Probability of a Series of Independent Events
| Probability | Repeat Times | |
|---|---|---|
| Event A | ||
| Event B |
Result
| P(Event A repeated n times) | |
| P(Event B repeated n times) | |
| Combined Probability (all events) |
Probability of a Normal Distribution
Find the area P under a normal distribution curve and confidence intervals.
Mean (μ)
Std Deviation (σ)
Left Bound (Lb)
Use -inf for −∞
Right Bound (Rb)
Use inf for +∞
Result
Conditional Probability (Bayes' Theorem)
Calculate P(A|B) using Bayes' Theorem: P(A|B) = P(B|A) × P(A) / P(B)
Probability of A: P(A)
Probability of B: P(B)
P(B|A) — B given A
Result
| P(A|B) — Probability of A given B | |
| P(A′|B) — Probability of NOT A given B | |
| P(A|B′) — Probability of A given NOT B |
Permutations & Combinations
Calculate permutations (nPr) and combinations (nCr) for given n and r values.
Total items (n)
Items chosen (r)
Result
| Permutations — nPr = n! / (n−r)! | |
| Combinations — nCr = n! / (r!(n−r)!) |
User Guide
How to Use:
- Select the calculator type you need
- Enter your probability values (between 0 and 1)
- Click Calculate to see results
- Export results as PDF using the Export button
Understanding Results:
- P(A′) — Complement (event NOT occurring)
- P(A∩B) — Intersection (both events occur)
- P(A∪B) — Union (either or both occur)
- P(A▵B) — Exclusive OR (one but not both)
- P(A|B) — Conditional (A given B)
Tips:
- All probability values must be between 0 and 1
- The Solver needs at least 2 values to compute the rest
- Use -inf and inf for infinite bounds in normal distribution
- For Bayes' theorem, P(B) must not be zero
Formulas
1. Complement:
P(A′) = 1 − P(A)
2. Intersection (independent):
P(A∩B) = P(A) × P(B)
3. Union:
P(A∪B) = P(A) + P(B) − P(A∩B)
4. Exclusive OR:
P(A▵B) = P(A∪B) − P(A∩B)
5. Series:
P = P(A)n × P(B)m × ...
6. Bayes' Theorem:
P(A|B) = P(B|A) × P(A) / P(B)
7. Normal Distribution:
P(Lb < X < Rb) = Φ((Rb−μ)/σ) − Φ((Lb−μ)/σ)
8. Permutations:
nPr = n! / (n−r)!
9. Combinations:
nCr = n! / (r!(n−r)!)
10. Confidence Interval:
CI = μ ± z × σ