Th e research objective was to obtain a fast/simple analytic solution for previously published Radiotherapy Tumor Control Probability (TCP) Integral Model by other authors . Finding, firstly, is a new/simpler Probability Function than Poisson distribution of survival clonogens which is developed from classical biological model algebraic/numerically modified equation. Solution obtained is t his Probability Function alternative based on a Binomial distribution equation approximation from literature. Result, t hus, is its use of for developing a fast/analytic solution of the 2D [ α and β biological modelling parameters ] Integral Model Cumulative TCP. The Gaussian Normal distribution convolution is implemented with th is P robability F unction into the integral model to sort longer/programming numerical methods and determine an analyt ical solution expression. As a complete result, a formulation for TCP based on Erf functions is obtained. Applications for radiotherapy treatment planning optimization improvements with biological models are explained.