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The figure displays several possible finite probability models for rolling a die. We can learn which model is actually accurate for a particular die only by rolling the die many times. However, some of the models are not valid. That is, they do not obey the rules. \begin{tabular}{|l|l|l|l|l|l|} \hline \multicolumn{6}{|c|}{Probability} \\ \hline Outcome & Madel 1 & Musel2 & Mudel) & Model 4 & \\ \hline & \( 1 / 7 \) & 13 & 1/3 & 1 & 2 \\ \hline & 17 & 1/6 & 1/6 & 1 & \\ \hline & 1,P & 1/4 & 1/6 & 2 & \\ \hline & 18 & 0 & 1/6 & 1 & \\ \hline & 1/7 & 1/6 & 1/6 & 1 & \\ \hline & 1/7 & 1/6 & 1/6 & 2 & \\ \hline \end{tabular} Which are valid and which are not? Select the best answer, with the correct explanation of what is wrong in the case of the invalid models. Model 2 is valid. Model 4 is not valid, because it has some probabilities that are greater than 1 . It is impossible to decide whether Models 1 and 3 are valid, since we do not know whether the events are disjoint. None of the given models is valid. Models 1, 3, and 4 have probabilities that do not sum to 1. Model 4 has some probabilities that are greater than 1 . Model 2 has some probabilities that do not match how a die works; for example, it is nonsensical that the probability of rolling a 4 is 0 . Only Model 2 is valid. Models 1,3 , and 4 have probabilities that do not sum to 1 . Model 4 has some probabilities that are greater than 1 . Models 1, 2, and 3 are valid. Model 4 is not valid, because it has some probabilities that are greater than 1 .

          The figure displays several possible finite probability models for rolling a die. We can learn which model is actually accurate for a particular die only by rolling the die many times. However, some of the models are not valid. That is, they do not obey the rules.
\begin{tabular}{|l|l|l|l|l|l|}
\hline \multicolumn{6}{|c|}{Probability} \\
\hline Outcome & Madel 1 & Musel2 & Mudel) & Model 4 & \\
\hline & \( 1 / 7 \) & 13 & 1/3 & 1 & 2 \\
\hline & 17 & 1/6 & 1/6 & 1 & \\
\hline & 1,P & 1/4 & 1/6 & 2 & \\
\hline & 18 & 0 & 1/6 & 1 & \\
\hline & 1/7 & 1/6 & 1/6 & 1 & \\
\hline & 1/7 & 1/6 & 1/6 & 2 & \\
\hline
\end{tabular}

Which are valid and which are not? Select the best answer, with the correct explanation of what is wrong in the case of the invalid models.
Model 2 is valid. Model 4 is not valid, because it has some probabilities that are greater than 1 . It is impossible to decide whether Models 1 and 3 are valid, since we do not know whether the events are disjoint.
None of the given models is valid. Models 1, 3, and 4 have probabilities that do not sum to 1. Model 4 has some probabilities that are greater than 1 . Model 2 has some probabilities that do not match how a die works; for example, it is nonsensical that the probability of rolling a 4 is 0 .
Only Model 2 is valid. Models 1,3 , and 4 have probabilities that do not sum to 1 . Model 4 has some probabilities that are greater than 1 .
Models 1, 2, and 3 are valid. Model 4 is not valid, because it has some probabilities that are greater than 1 .

The figure displays several possible finite probability models for rolling a die. We can learn which model is actually accurate for a particular die only by rolling the die many times. However, some of the models are not valid. That is, they do not obey the rules.

6|c|Probability

Outcome Madel 1 Musel2 Mudel) Model 4

1 / 7 13 1/3 1 2

17 1/6 1/6 1

1,P 1/4 1/6 2

18 0 1/6 1

1/7 1/6 1/6 1

1/7 1/6 1/6 2

Which are valid and which are not? Select the best answer, with the correct explanation of what is wrong in the case of the invalid models.
Model 2 is valid. Model 4 is not valid, because it has some probabilities that are greater than 1 . It is impossible to decide whether Models 1 and 3 are valid, since we do not know whether the events are disjoint.
None of the given models is valid. Models 1, 3, and 4 have probabilities that do not sum to 1. Model 4 has some probabilities that are greater than 1 . Model 2 has some probabilities that do not match how a die works; for example, it is nonsensical that the probability of rolling a 4 is 0 .
Only Model 2 is valid. Models 1,3 , and 4 have probabilities that do not sum to 1 . Model 4 has some probabilities that are greater than 1 .
Models 1, 2, and 3 are valid. Model 4 is not valid, because it has some probabilities that are greater than 1 .

Added by Joel W.

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