if pointer 1 is spun and then pointer 2 is spun, determine the probability of landing on a color other than green on both spins.

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Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Spinner Probability", "Independent Events" ], "new_concepts": [], "current_concepts": [ "Spinner Probability", "Independent Events", "Complementary Events" ] } ## Analyze Pointer 1 Using the **Spinner Probability** knowledge point $$ \begin{aligned} &\text{Total sectors} = 4 \quad (\text{Green, Red, Yellow, Yellow})\ &\text{Green sectors} = 1\ &P(\text{Green on 1}) = \frac{1}{4}\ &P(\text{Not Green on 1}) = 1 - \frac{1}{4} = \frac{3}{4} \end{aligned} $$ ## Analyze Pointer 2 Using the **Spinner Probability** knowledge point $$ \begin{aligned} &\text{Total sectors} = 8 \quad (\text{Green, Green, Red, Red, Red, Yellow, Yellow, Yellow})\ &\text{Green sectors} = 2\ &P(\text{Green on 2}) = \frac{2}{8} = \frac{1}{4}\ &P(\text{Not Green on 2}) = 1 - \frac{1}{4} = \frac{3}{4} \end{aligned} $$ ## Calculate joint probability Using the **Independent Events** knowledge point $$ \begin{aligned} P(\text{Not Green on both}) &= P(\text{Not Green on 1}) \cdot P(\text{Not Green on 2})\ &= \frac{3}{4} \cdot \frac{3}{4}\ &= \frac{9}{16} \end{aligned} $$ If pointer 1 is spun and then pointer 2 is spun, determine the probability of landing on a color other than green on both spins. The probability is $\frac{9}{16}$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Statistics", "Probability of Independent Events" ] }

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Explanation:

Analyze Pointer 1

Analyze Pointer 2

Calculate joint probability

Answer: