# Probability Calculator (Two Events)

URL: https://speedycalculator.com/calculators/statistics/probability/
Last updated: 2026-10-25

> The probability calculator finds the probability of A and B, A or B, neither and exactly one, for two independent events with known probabilities.

## Inputs

- P(A) (%)
- P(B) (%)

## Results

- P(A and B)
- P(A or B)
- P(neither)
- P(exactly one)

## Formula

```
P(A ∩ B) = P(A)P(B)
P(A ∪ B) = P(A) + P(B) − P(A)P(B)
```

## Explanation

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

FieldWhat to enterP(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) (%)257.537.511.25501562.518.757522.510030

## 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 %.

## FAQ

**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).