In Kleen City on Thursday night, half of the TV audience...

Name: Problem 10, Chapter 3: Probability, Statistics, and Queuing Theory with Computer Science Applications, Second Edition (Computer Science and Scientific Computing)
Uploaded: 2020-08-18T14:28:18-08:00
Duration: 1 min 51 s
Channel: Kerry Thornton-Genova
Description: In Kleen City on Thursday night, half of the TV audience watches Channel 6, 40 percent watches Channel 12 , and the remaining 10 percent watch Channel 13 (a channel for the lucky!). Find the probability that of 10 Thursday night TV viewers, 5 will be watching Channel 6 , 4 will be looking at Channel 12 , and one will be viewing Channel 13 .

In Kleen City on Thursday night, half of the TV audience watches Channel 6, 40 percent watches Channel 12 , and the remaining 10 percent watch Channel 13 (a channel for the lucky!). Find the probability that of 10 Thursday night TV viewers, 5 will be watching Channel 6 , 4 will be looking at Channel 12 , and one will be viewing Channel 13 .

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Key Concepts

Multinomial Distribution

The multinomial distribution is a generalization of the binomial distribution that applies to experiments where each trial has more than two possible outcomes. It provides a framework for calculating the probability of obtaining a specific combination of outcomes over a fixed number of independent trials, each with its own probability of occurrence.

Multinomial Coefficient

The multinomial coefficient is used to determine the number of ways in which a given set of outcomes can occur in a sequence of independent trials. It is computed as the factorial of the total number of trials divided by the product of the factorials of the counts for each outcome, which accounts for the different arrangements of these outcomes.

Independence of Trials

Independence of trials means that the outcome of any particular trial does not affect the outcome of any other trial. This assumption is crucial for properly applying the multinomial distribution, as it allows the probability of any combination of outcomes to be found by multiplying the probabilities of the individual outcomes.

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