The following table shows the distribution of murders by type of weapon for murder cases in a particular country over the past 12 years. Complete parts (a) through (e)
\begin{tabular}{lr}
Weapon & Probability \\
Handgun & 0.477 \\
\hline Rifle & 0.027 \\
\hline Shotgun & 0.033 \\
\hline Unknown firearm & 0.148 \\
\hline Knives & 0.132 \\
\hline Hands, fists, etc. & 0.054 \\
\hline Other & 0.129
\end{tabular}
(a) Is the given table a probability model? Why or why not?
A. No, the sum of the probabilities of all outcomes does not equal 1 .
B. No, the probability of all events in the table is not greater than or equal to 0 and less than or equal to 1
C. No; the probability of all events in the table is not greater than or equal to 0 and less than or equal to 1 , and the sum of the probabilities of all outcomes does
D. Yes; the rules required for a probability model are both met.
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Final Answer: \(\boxed{\text{D. Yes; the rules required for a probability model are both met.}}\)
Step 1 ：First, we need to check if the probability of each event is between 0 and 1, inclusive. The probabilities for each type of weapon are as follows: handgun = 0.477, rifle = 0.027, shotgun = 0.033, unknown firearm = 0.148, knives = 0.132, hands, fists, etc. = 0.054, other = 0.129. All these probabilities are between 0 and 1, inclusive.
Step 2 ：Second, we need to check if the sum of the probabilities of all outcomes equals 1. The sum of the probabilities is \(0.477 + 0.027 + 0.033 + 0.148 + 0.132 + 0.054 + 0.129 = 1.0\).
Step 3 ：Since all the probabilities are between 0 and 1, inclusive, and the sum of the probabilities of all outcomes equals 1, the given table is a probability model.
Step 4 ：Final Answer: \(\boxed{\text{D. Yes; the rules required for a probability model are both met.}}\)
