Multinomial Formula Probability. In probability theory the multinomial distribution is a generalization of the binomial distribution. When k is 2 and n.
Thus p 1 0 25 p 2 0 25 p 3 0 25 and p 4 0 25. The distribution of bs y y 1 y 2 ldots y k is called the multinomial distributionwith parameters n and bs p p 1 p 2 ldots p k. When k is 2 and n.
P k n k.
P 1 n 1 p 2 n 2. We plug these inputs into the multinomial formula as shown below. Obviously k 1 k 2 cdots k m n p 1 p 2 cdots p m 1. For n independent trials each of which leads to a success for exactly one of k categories with each category having a given fixed success probability the multinomial distribution gives the probability of any particular combination of numbers of successes for the various categories.
