Binomial vs Geometric — Same Ω (v2)

Two observers, one sample space

Same binary Ω — different equivalence relations — different quotient geometries

Ω — 40 binary sequences of length 10 | p(black) = 0.50

X = count of black dots

ω ~ ω′ iff same total → Binomial(K, p)

Y = position of first black dot

ω ~ ω′ iff first black at same slot → Geometric(p)

N (sequences) 40 K (length) 10 p 0.50

empirical proportion

theoretical PMF