FIT / MATHS LAB
JC · H2Round 1/6Score 0
Distribution Duel
Distribution challenge
Concept figure
Live probability analysis
Adjust the parameters and examine both plots.
The maths
Binomial: P(X = x) = C(n,x)pˣ(1−p)ⁿ⁻ˣ. E(X) = np and Var(X) = np(1−p).
Normal: Z = (X−μ)/σ and F(x) = Φ((x−μ)/σ). The shaded density area is a probability, not a bar height.
Conditional: P(A | B) = P(A∩B)/P(B). Events A and B are independent if P(A∩B) = P(A)P(B).
Numerical method: normal probabilities use a polynomial approximation to erf with maximum absolute error about 1.5 × 10⁻⁷. Binomial probabilities use a stable recurrence.