Binomial Free-Throw Challenge

Choose n shots and success chance p, guess the makes, then simulate. (A binomial model of n Bernoulli trials.)
Discrete Distribution: Binomial(n, p)
Score = 100 − 10×|guess − actual| (min 0)
Expected makes E[X]=np
Variance Var[X]=np(1−p)
St.dev
Round Result
Total Score 0
Empirical Distribution (Simulated) vs Theoretical PMF 0 sims
Bars show relative frequency of total makes X~Binomial(n,p). Blue = simulation; amber = exact binomial P(X=k)=C(n,k)p^k(1−p)^(n−k).
What you’re modeling: When outcomes are countable, the binomial distribution counts successes across a fixed number of independent trials with constant success chance p. Try changing n and p and watch the histogram shift: bigger n narrows the spread (relative), while p moves the center.