Clebsch-Gordan coefficients and the binomial distribution

Abstract

A class of Clebsch-Gordan coefficients are derived from the properties of conditional probability using the binomial distribution. In particular, in the case of $l=l_1+l_2$ it is shown that $$[<l_1/2-k_1,l_2/2-k_2|l/2,k=k_1+k_2]{>}^2=\frac{(\begin{array}{c}{l}_1{k}_1\end{array})(\begin{array}{c}{l}_2{k}_2\end{array})}{(\begin{array}{c}lk\end{array})}$$

6 pages, latex