Why is the following not a probability model? Color Probability Red 0.3

Name: Problem 9, Chapter 5: Statistics Informed Decisions Using Data
Uploaded: 2023-01-12T22:02:54-08:00
Channel: Emily Himsel
Description: Why is the following not a probability model? Color Probability Red 0.3 Green -0.3 Blue 0.2 Brown 0.4 Yellow 0.2 Orange 0.2

step 1 So first we need to find the sum of the probabilities to determine if this is an okay method or

Question

Why is the following not a probability model? $$ \begin{array}{lc} \text { Color } & \text { Probability } \\ \hline \text { Red } & 0.3 \\ \hline \text { Green } & -0.3 \\ \hline \text { Blue } & 0.2 \\ \hline \text { Brown } & 0.4 \\ \hline \text { Yellow } & 0.2 \\ \hline \text { Orange } & 0.2 \\ \hline \end{array} $$

   Why is the following not a probability model?
$$
\begin{array}{lc}
\text { Color } & \text { Probability } \\
\hline \text { Red } & 0.3 \\
\hline \text { Green } & -0.3 \\
\hline \text { Blue } & 0.2 \\
\hline \text { Brown } & 0.4 \\
\hline \text { Yellow } & 0.2 \\
\hline \text { Orange } & 0.2 \\
\hline
\end{array}
$$

Statistics Informed Decisions Using Data

Michael Sullivan III 5th Edition

Chapter 5, Problem 9

Instant Answer

Solved by Expert Emily Himsel

01/12/2023

Step 1

The sum of the probabilities should be equal to 1 in a probability model. In this case, the sum of the probabilities is indeed 1. Show more…

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Why is the following not a probability model? $$ \begin{array}{lc} \text { Color } & \text { Probability } \\ \hline \text { Red } & 0.3 \\ \hline \text { Green } & -0.3 \\ \hline \text { Blue } & 0.2 \\ \hline \text { Brown } & 0.4 \\ \hline \text { Yellow } & 0.2 \\ \hline \text { Orange } & 0.2 \\ \hline \end{array} $$

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Key Concepts

Normalization

For any probability model, the sum of the probabilities assigned to all possible outcomes must equal one. This property, known as normalization, ensures that the model accounts for the entire sample space and that the total measure of all outcomes is complete.

Probability Model

A probability model is a mathematical construct that assigns a numerical value (probability) to each outcome in a sample space with the requirement that each probability is non-negative and the sum of all probabilities is equal to one. This ensures that the model is a valid representation of randomness and reflects the certainty that one outcome must occur.

Non-Negativity

A fundamental axiom of probability is that probabilities must be non-negative, meaning that no event can have a probability less than zero. Negative values do not make sense in the interpretation of likelihood or frequency and violate the basic principles of probability theory.

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