In probability theory and statistics, the binomial distribution is the discrete probability distribution of the number of successes in a sequence of n independent yes/no experiments, each of which yields success with probability p.The binomial probability formula is given by? nC?_x p^(x ) q^(n-x); where p, represents the probability of success, and q = 1-p, represents the probability of failure; x=0,2,3……..,n, representing the random variable of the number of success in n trials. For each value the random variable assumes, say x, the corresponding probability is computed by substituting x in the binomial probability formula. A formula, which is a direct derivative of the given binomial probability formula, is however proposed in this paper which gives f(x+1) as a function of f(x), once f(o)=q^n is computed. With this it will no longer be necessary to fall back on the binomial probability formula and make substitution for each value of x to compute the probabilities independently for x greater than 0, and less than or equal to n (0