Probability Explorer

Interactive binomial distribution visualiser.

What Is This?

The binomial distribution answers this question: "If I repeat a yes/no experiment N times, where each trial has probability P of success, how likely is it that I get exactly K successes?"

Examples: flipping a coin 100 times and asking how likely is exactly 53 heads. Shooting 20 free throws at 75% and asking how likely is missing 4. Testing 50 products at 2% defect rate.

Key concepts
N (trials):How many times you repeat the experiment.
P (probability):Chance of success on any single trial (0 = never, 1 = always).
Mean μ = N×P:The average number of successes you expect.
Normal approx:When N is large, the curve approximates a bell curve (Central Limit Theorem).
Quick Examples
Parameters
N: Number of trials50
5200
P: Probability of success per trial0.50
0.010.99
Mean μ = N×P25.00
Variance σ² = NPQ12.50
Std Dev σ3.54
Mode25
Distribution: P(X = k)
04812162024283236404448
Binomial P(X = k) Normal approximation