the math department is putting together an order for new calculators. the students are asked what model and color they prefer.

which statement about the students preferences is true?

a. more students prefer black calculators than silver calculators.
b. more students prefer model 66 calculators than model 55 calculators.
c. the fewest students prefer silver model 66 calculators.
d. more students prefer silver model 55 calculators than silver model 77 calculators.

Question

the math department is putting together an order for new calculators. the students are asked what model and color they prefer.

which statement about the students preferences is true?

a. more students prefer black calculators than silver calculators.
b. more students prefer model 66 calculators than model 55 calculators.
c. the fewest students prefer silver model 66 calculators.
d. more students prefer silver model 55 calculators than silver model 77 calculators.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Two-Way Relative Frequency Tables" ], "new_concepts": [], "current_concepts": [ "Two-Way Relative Frequency Tables", "Marginal Frequency", "Joint Relative Frequency" ] } ## Analyze option A $$ \begin{aligned} P(\text{Black}) &= 0.10 \ P(\text{Silver}) &= 0.90 \ 0.10 &< 0.90 \end{aligned} $$ ## Analyze option B $$ \begin{aligned} P(\text{Model 66}) &= 0.43 \ P(\text{Model 55}) &= 0.25 \ 0.43 &> 0.25 \end{aligned} $$ ## Analyze options C and D $$ \begin{aligned} P(\text{Silver} \cap \text{Model 66}) &= 0.40 \quad (\text{highest among silver}) \ P(\text{Silver} \cap \text{Model 55}) &= 0.20 \ P(\text{Silver} \cap \text{Model 77}) &= 0.30 \ 0.20 &< 0.30 \end{aligned} $$

A. More students prefer black calculators than silver calculators.

B. More students prefer Model 66 calculators than Model 55 calculators.

C. The fewest students prefer silver Model 66 calculators.

D. More students prefer silver Model 55 calculators than silver Model 77 calculators.

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Statistics", "Two-Way Relative Frequency Tables" ] }

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QUESTION IMAGE

Question

Explanation:

Analyze option A

Analyze option B

Analyze options C and D

Answer: