g.pr.10.1 (mc)

a study was conducted on 465 people to find their favorite genre of music. a two-way table below shows the results according to their age. find p(country \cup 36-50).

Question

g.pr.10.1 (mc)

a study was conducted on 465 people to find their favorite genre of music. a two-way table below shows the results according to their age. find p(country \cup 36-50).

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Two-Way Tables", "Addition Rule for Probability" ], "new_concepts": [], "current_concepts": [ "Two-Way Tables", "Addition Rule for Probability" ] } ## Calculate the individual and intersection counts $$ \begin{aligned} &\text{Total sample size } (N) = 465\ &\text{Total Country} = 22 + 30 + 28 + 42 = 122\ &\text{Total 36-50} = 30 + 28 + 38 + 20 = 116\ &\text{Country} \cap \text{36-50} = 28 \end{aligned} $$ ## Apply the addition rule for probability $$ \begin{aligned} P(\text{Country} \cup \text{36-50}) &= P(\text{Country}) + P(\text{36-50}) - P(\text{Country} \cap \text{36-50})\ &= \frac{122}{465} + \frac{116}{465} - \frac{28}{465}\ &= \frac{122 + 116 - 28}{465}\ &= \frac{210}{465} \end{aligned} $$ ## Simplify the fraction $$ \begin{aligned} \frac{210}{465} = \frac{210 \div 15}{465 \div 15} = \frac{14}{31} \approx 0.4516 \end{aligned} $$ $\frac{14}{31}$ (or approximately $0.452$) { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Statistics", "Addition Rule for Probability" ] }

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Question

Explanation:

Calculate the individual and intersection counts

Apply the addition rule for probability

Simplify the fraction

Answer: