Chapter 5.2, Problem 42BB

Multinomial Distribution The binomial distribution applies only to cases involving two types of outcomes, whereas the multinomial distribution involves more than two categories. Suppose we have three types of mutually exclusive outcomes denoted by A, B. and C. Let P(A) = p₁, P(B) = p₂, and P(C) = p₃. In n independent trials, the probability of x₁ outcomes of type A, x₂ outcomes of type B, and x₃ outcomes of type C is given by

$\frac{n!}{(x_1)!(x_2)!(x_3)!}•{{\displaystyle P}}_1^{x_1}•{{\displaystyle P}}_2^{x_2}•{{\displaystyle P}}_3^{x_3}$

A roulette wheel in the Venetian casino in Las Vegas has 18 red slots, 18 black slots, and 2 green slots. If roulette is played 15 times, find the probability of getting 7 red outcomes, 6 black outcomes, and 2 green outcomes.