Solution Found!
Hypergeometric Distribution If we sample from a small
Chapter 5, Problem 46BB(choose chapter or problem)
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 \(P(A)=p 1, P(B)=p 2, \text { and } P(C)=p 3\). In n independent trials, the probability of x 1 outcomes of type A, x 2 outcomes of type B, and x 3 outcomes of type C is given by
\(n !(x 1) !(x 2) !(x 3) ! \cdot p 1 \times 1 \cdot p 2 \times 2 \cdot p 3 \times 3\)
A roulette wheel in the Hard Rock casino in Las Vegas has 18 red slots, 18 black slots, and 2 green slots. If roulette is played 12 times, find the probability of getting 5 red outcomes, 4 black outcomes, and 3 green outcomes.
Equation Transcription:
Text Transcription:
P (A) =p 1, P(B)=p2, and P (C)=p3
n! (x 1) ! (x 2) ! (x 3) ! \cdot p 1 x 1 \cdot p 2 x 2 \cdot p 3 x 3
Questions & Answers
QUESTION:
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 \(P(A)=p 1, P(B)=p 2, \text { and } P(C)=p 3\). In n independent trials, the probability of x 1 outcomes of type A, x 2 outcomes of type B, and x 3 outcomes of type C is given by
\(n !(x 1) !(x 2) !(x 3) ! \cdot p 1 \times 1 \cdot p 2 \times 2 \cdot p 3 \times 3\)
A roulette wheel in the Hard Rock casino in Las Vegas has 18 red slots, 18 black slots, and 2 green slots. If roulette is played 12 times, find the probability of getting 5 red outcomes, 4 black outcomes, and 3 green outcomes.
Equation Transcription:
Text Transcription:
P (A) =p 1, P(B)=p2, and P (C)=p3
n! (x 1) ! (x 2) ! (x 3) ! \cdot p 1 x 1 \cdot p 2 x 2 \cdot p 3 x 3
ANSWER: