log(p / 1-p) = beta

p / 1-p = exp(beta)

p = exp(beta) - p(exp(beta))

p + p(exp(beta)) = exp(beta)

p(1 + exp(beta)) = exp(beta)

p = exp(beta) / (1 + exp(beta))

p = 1 / (1/exp(beta) + 1)

p = 1 / (1 + 1/exp(beta))

p = 1 / (1 + exp(-beta))
