Probability Calculator
Calculate single-event probability, combine two events with AND/OR rules, or find experimental relative frequency — with full step-by-step working.
Step-by-step solution
Enter values and press Calculate
Probability Calculator Explained
Core concepts, classroom applications, and plain-English explanations for all audiences.
Probability isn't just dice — it's everywhere
When the weather forecast says "70% chance of rain," that's probability. When your car insurance costs more because you're 18, that's an insurer calculating the probability you'll make a claim. When a doctor says a test is "95% accurate," that probability has a specific mathematical meaning. Understanding it isn't optional — it's how the world actually works.
Worked example
"A bag contains 4 red, 3 blue and 5 green counters. What's the probability of picking red at random?"
Total outcomes: 4 + 3 + 5 = 12
Favourable outcomes (red): 4
P(red) = 4/12 = 1/3
As a decimal: 0.333...
As a percentage: 33.3%
All three forms — fraction, decimal, percentage — mean the same thing. Know which one a question asks for.
Real-world probability in action
- → Weather forecasts: "70% chance of rain" means in similar conditions, it rained 7 out of 10 times historically. It's relative frequency, not certainty.
- → Quality control: a factory tests 200 products and finds 3 defective. Relative frequency = 3/200 = 1.5% defect rate. They use this to predict future batches.
- → Sports betting: odds of 4/1 on a horse imply a probability of 1/5 = 20%. The bookmaker's margin means the total probabilities across all horses sum to more than 1. That's why the house always wins.
The AND/OR shortcut
For independent events: P(A AND B) = P(A) × P(B). For mutually exclusive events: P(A OR B) = P(A) + P(B). "AND" means multiply. "OR" usually means add — but only when events can't both happen at once.
Probability explained
What is probability?
A number between 0 and 1 that measures how likely an event is. 0 = impossible, 1 = certain. Written as a fraction, decimal, or percentage.
P(event) = favourable outcomes ÷ total outcomes.
The AND / OR rules
P(A and B) = P(A) × P(B) for independent events. P(A or B) = P(A) + P(B) for mutually exclusive events.
General OR: P(A ∪ B) = P(A) + P(B) − P(A ∩ B).
Theoretical vs experimental
Theoretical probability is what maths predicts. Experimental (relative frequency) is what actually happened in trials.
More trials → closer to theoretical (Law of Large Numbers).