Probability Visualizer

Learn probability from the ground up using coins, dice, playing cards, spinners, and colored balls in a bag. Each section shows sample space, favorable outcomes, theoretical probability, and simulation results.

🪙 Coins 🎲 Dice 🂡 Cards 🎡 Spinner 🔴 Bag Draws 📈 Simulation

Interactive probability lab

Open a section, choose an event, and compare the exact answer with simulation.

Theory + Simulation Friendly examples

Coin toss visualizer

Start with one or two fair coins. Then ask events like exactly one head, at least one tail, or both same.

Sample space is small and perfect for beginners

Dice visualizer

Study one die or two dice. Explore even numbers, prime faces, sums, doubles, and more.

Great for events with many outcomes

Playing cards visualizer

Draw one card from a standard 52-card deck. Explore red, black, face cards, suits, aces, hearts, spades, and more.

Classical probability with 52 equally likely outcomes

Spinner probability

A spinner helps explain probability through sectors. Larger sectors mean larger probability.

Area-based intuition

Colored balls in a bag

This is a powerful model for probability. You can change the bag composition and study single-draw probability.

Flexible and highly visual

More probability ideas

These extra examples make the visualizer richer and more useful.

Beyond the basics
1. Complement rule

Sometimes it is easier to calculate the probability that an event does not happen.

P(not A) = 1 - P(A)

Example: with one die, probability of getting a number greater than 4 is 2/6 = 1/3. So probability of not getting a number greater than 4 is 1 - 1/3 = 2/3.

2. Experimental probability

The simulation buttons on this page estimate probability by actually performing many random trials.

Experimental probability = number of successes / number of trials
3. Independent events

If two events do not affect each other, multiply their probabilities.

P(A and B) = P(A) × P(B)

Example: probability of head on a coin and 6 on a die = 1/2 × 1/6 = 1/12.

4. Conditional probability idea

When information changes the sample space, probability changes too.

P(A | B) = P(A and B) / P(B)

Example: from a deck of cards, probability of drawing a king given the card is face card = 4/12 = 1/3.

5. Expected value intuition

Expected value is the long-run average outcome of a random experiment.

For one fair die: (1+2+3+4+5+6)/6 = 3.5

Bayes visualizer

Bayes' theorem updates probability after new evidence arrives. This is useful in medical tests, spam detection, fraud checks, and machine learning.

Prior → evidence → posterior
Bayes theorem: P(A | B) = P(B | A) × P(A) / P(B)

Think of A as a hidden condition and B as observed evidence. Example: A = person has a disease, B = test is positive.

@copy; Champak Roy