Probability Calculator - Calculate Probability of Events Online

Calculate the probability of any event with our free online probability calculator. Find simple, complementary, and conditional probabilities with formula explanations.

Calculation Type

Favorable Outcomes

Total Outcomes

Examples:

Understanding Probability

Probability measures how likely an event is to occur, expressed as a number between 0 and 1. Zero means impossible, one means certain, and values in between represent varying degrees of likelihood. We use probability every day - from weather forecasts to game strategies to risk assessments.

The beauty of probability is that it turns uncertainty into something we can calculate with. Whether you're playing cards, investing in stocks, or deciding whether to carry an umbrella, probability helps you make informed decisions.

Probability Formulas

Simple Probability

P(E) = Favorable / Total

The basic formula: count favorable outcomes, divide by total possible outcomes.

Complement

P(A') = 1 - P(A)

The probability an event does NOT happen. Useful when "not happening" is easier to calculate.

Conditional

P(B|A) = P(A∩B) / P(A)

Probability of B given that A already happened. The foundation of Bayesian reasoning.

Worked Examples

Example 1: Drawing a Card

What's the probability of drawing an Ace from a standard 52-card deck?

Favorable outcomes: 4 (four Aces)

Total outcomes: 52 (cards in deck)

P(Ace) = 4/52 = 1/13 ≈ 0.0769

About 7.69% chance of drawing an Ace

Example 2: Rolling Dice

What's the probability of rolling a 6 on a fair six-sided die?

Favorable outcomes: 1 (just the 6)

Total outcomes: 6 (numbers 1-6)

P(6) = 1/6 ≈ 0.1667

About 16.67% chance

Example 3: Complement - Not Rolling a 6

What's the probability of NOT rolling a 6?

P(rolling 6) = 1/6

P(not 6) = 1 - P(6)

P(not 6) = 1 - 1/6 = 5/6 ≈ 0.8333

About 83.33% chance of not rolling a 6

Example 4: Conditional Probability

In a class, 50% study math (A), and 20% study both math and physics (A∩B). Given a student studies math, what's the probability they also study physics?

P(A) = 0.50, P(A∩B) = 0.20

P(B|A) = P(A∩B) / P(A)

P(B|A) = 0.20 / 0.50 = 0.40

40% of math students also study physics

Example 5: Roulette

American roulette has 38 slots (18 red, 18 black, 2 green). What's the probability of landing on red?

Favorable: 18 red slots

Total: 38 slots

P(red) = 18/38 = 9/19 ≈ 0.4737

About 47.37% - less than 50% due to green slots

Quick Fact

Probability theory began with a gambling problem. In 1654, French nobleman Chevalier de Méré asked mathematician Blaise Pascal why he lost money betting he could roll at least one 6 in 4 dice rolls. Pascal's correspondence with Pierre de Fermat solving this problem founded probability theory. Their work showed the probability was 1 - (5/6)⁴ ≈ 51.77%, explaining his losses over time.

Frequently Asked Questions

What does probability 0.5 mean?

A probability of 0.5 (or 50%) means the event is equally likely to happen or not happen - like a fair coin flip. Over many trials, you'd expect the event to occur about half the time, though short-term results can vary significantly.

What's the difference between probability and odds?

Probability is favorable/total (ranges 0-1). Odds are favorable:unfavorable. If P = 1/4, odds are 1:3. To convert: odds = P/(1-P). Gamblers use odds; statisticians use probability. Both describe likelihood, just differently.

Can probability be greater than 1?

No, probability is always between 0 and 1 (or 0% to 100%). If you calculate a probability outside this range, there's an error. This is a fundamental axiom of probability theory - it's mathematically impossible for a valid probability to exceed 1.

What's the probability of two independent events both happening?

Multiply their individual probabilities: P(A and B) = P(A) × P(B). For example, probability of two heads in a row: 0.5 × 0.5 = 0.25 (25%). This only works for independent events where one doesn't affect the other.

What is the law of large numbers?

As you repeat a random experiment more times, the observed frequency approaches the theoretical probability. Flip a coin 10 times - might get 7 heads. Flip it 10,000 times - you'll get very close to 5,000 heads (50%).

Where is probability used in real life?

Everywhere: weather forecasting (30% chance of rain), insurance (calculating premiums), medicine (test accuracy, treatment success), finance (risk assessment), sports (batting averages), quality control, machine learning, and game theory.

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