Combining probabilities correctly avoids common mistakes such as adding when you should multiply.
How to use the Probability Calculator
- P(A)
- P(B)
Results update as you type, and every field accepts the units shown in its menu.
How it works
For independent events, multiply probabilities for “and”; use inclusion–exclusion for “or”.
Inputs explained
| Field | What to enter |
|---|---|
| P(A) | In % |
| P(B) | In % |
What each result means
- P(A and B) = [P(A)]×[P(B)]÷100
- P(A or B) = [P(A)] + [P(B)] – [P(A)]×[P(B)]÷100
- P(neither) = (100 – [P(A)])×(100 – [P(B)])÷100
- P(exactly one) = [P(A)] + [P(B)] – 2×[P(A)]×[P(B)]÷100
Example values
How the main result changes when P(A) changes and everything else stays at the example values above:
| P(A) (%) | P(A and B) (%) |
|---|---|
| 25 | 7.5 |
| 37.5 | 11.25 |
| 50 | 15 |
| 62.5 | 18.75 |
| 75 | 22.5 |
| 100 | 30 |
Formula
P(A ∩ B) = P(A)P(B)P(A ∪ B) = P(A) + P(B) − P(A)P(B)Worked example
Inputs — P(A): 50 %; P(B): 30 %.
Results — P(A and B) = 15 %; P(A or B) = 65 %; P(neither) = 35 %; P(exactly one) = 50 %.
Frequently asked questions
What if events are not independent?
Use P(A and B) = P(A) × P(B | A) with the conditional probability.
Can probabilities exceed 100%?
No; if “or” seems to, check for double counting.
What formula does the Probability Calculator use?
P(A ∩ B) = P(A)P(B).