insurance company executives surveyed 200 young adults about their first motor vehicle. the results are shown in the two-way table.

\begin{tabular}{|c|c|c|c|c|}
\hline
\multicolumn{2}{|c|}{} & \multicolumn{3}{c|}{motor vehicle} \\
\cline{3-5}
\multicolumn{2}{|c|}{} & car & truck & suv \\
\hline
\multirow{3}{*}{cylinders} & four & 118 & 6 & 18 \\
\cline{2-5}
& six & 16 & 12 & 20 \\
\cline{2-5}
& eight & 2 & 6 & 2 \\
\hline
\end{tabular}

a survey participant is randomly selected. let $e$ be the event that the participants first motor vehicle had eight cylinders and let $t$ be the event that the participants first motor vehicle was a truck. what is the value of $p(e \text{ or } t)$?

Question

insurance company executives surveyed 200 young adults about their first motor vehicle. the results are shown in the two-way table.

\begin{tabular}{|c|c|c|c|c|}
\hline
\multicolumn{2}{|c|}{} & \multicolumn{3}{c|}{motor vehicle} \\
\cline{3-5}
\multicolumn{2}{|c|}{} & car & truck & suv \\
\hline
\multirow{3}{*}{cylinders} & four & 118 & 6 & 18 \\
\cline{2-5}
& six & 16 & 12 & 20 \\
\cline{2-5}
& eight & 2 & 6 & 2 \\
\hline
\end{tabular}

a survey participant is randomly selected. let $e$ be the event that the participants first motor vehicle had eight cylinders and let $t$ be the event that the participants first motor vehicle was a truck. what is the value of $p(e \text{ or } t)$?

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Classical Probability" ], "new_concepts": [], "current_concepts": [ "Classical Probability", "Two-Way Tables", "Addition Rule for Probability" ] } ## Calculate the individual and intersection probabilities $$ \begin{aligned} &\text{Total surveyed } (N) = 200\ &n(E) = 2 + 6 + 2 = 10\ &n(T) = 6 + 12 + 6 = 24\ &n(E \cap T) = 6\ &P(E) = \frac{10}{200} = 0.05\ &P(T) = \frac{24}{200} = 0.12\ &P(E \cap T) = \frac{6}{200} = 0.03 \end{aligned} $$ ## Apply the addition rule for probability $$ \begin{aligned} P(E \text{ or } T) &= P(E) + P(T) - P(E \cap T)\ &= 0.05 + 0.12 - 0.03\ &= 0.14 \end{aligned} $$

0.14

0.17

0.03

0.28

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Statistics", "Addition Rule for Probability" ] }

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QUESTION IMAGE

Question

Explanation:

Calculate the individual and intersection probabilities

Apply the addition rule for probability

Answer: