All calculatorsProbability Calculator
Calculate probabilities fast using single events, AND (intersection), OR (union), and conditional probability, with optional step-by-step. Perfect for intro probability and statistics homework.
Background
Probability is a number between 0 and 1. You’ll mostly use a few core rules: P(A∩B) (AND), P(A∪B) (OR), and P(A|B) (conditional). This calculator helps you plug in what you know and outputs the correct result with clear steps.
How to use this calculator
- Choose what you want to compute: P(A), P(A∩B), P(A∪B), or P(A|B).
- Choose input style: probability (0–1 / %) or outcomes (favorable / total).
- Enter values (and extra info if requested), then click Calculate.
- Use Quick picks to load common exam setups instantly.
How this calculator works
- Normalizes inputs to probabilities between 0 and 1.
- Uses the correct rule for the selected mode: AND, OR, or conditional probability.
- Supports independent AND by multiplying probabilities, or accepts a provided P(A∩B).
- For OR, uses P(A∪B)=P(A)+P(B)-P(A∩B) unless mutually exclusive is checked.
- For conditional probability, computes P(A|B)=P(A∩B)/P(B) and validates P(B)>0.
Formula & Equation Used
Single event: P(A)=\dfrac{\text{favorable}}{\text{total}}
AND (independent): P(A∩B)=P(A)\cdot P(B)
OR (general): P(A∪B)=P(A)+P(B)-P(A∩B)
Conditional: P(A|B)=\dfrac{P(A∩B)}{P(B)}
Example Problems & Step-by-Step Solutions
Example 1 — Single event (die)
What’s the probability of rolling a 1 on a fair six-sided die?
- Favorable outcomes = 1 (rolling 1).
- Total outcomes = 6.
- P(A)=1/6≈0.1667=16.67%
Example 2 — AND (independent coins)
Flip two fair coins. What’s the probability of heads on both?
- P(H)=1/2 for each coin.
- Independent AND: P(H∩H)=(1/2)(1/2)=1/4.
Example 3 — Conditional probability
Given P(A)=0.30, P(B)=0.40, and P(A∩B)=0.12, find P(A|B).
- Use P(A|B)=P(A∩B)/P(B).
- P(A|B)=0.12/0.40=0.30.
Frequently Asked Questions
Q: What’s the difference between AND and OR?
AND means both happen (A∩B), OR means at least one happens (A∪B).
Q: When can I add probabilities for OR?
Only if events are mutually exclusive (no overlap). Otherwise subtract the overlap: P(A∪B)=P(A)+P(B)-P(A∩B).
Q: Why can’t P(A|B) use P(B)=0?
Because conditional probability divides by P(B). If P(B)=0, the condition “B happened” can’t occur.
Q: Can I enter percentages?
Yes. Type 25% and it will be treated as 0.25.
Q: Does this calculator do distributions?
MVP: no. This tool focuses on core probability rules (single, AND/OR, conditional).
