Probability Calculator
Probability Calculator Calculate the probability of events, unions, intersections, normal distributions, and more.
Modify the values and click Calculate to get instant results.
i
Modify the values and click the Calculate button to use
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
ProbabilityRepeat 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:

  1. Select the calculator type you need
  2. Enter your probability values (between 0 and 1)
  3. Click Calculate to see results
  4. 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