if the pointer in the figure is spun twice, find the probability that the pointer lands on green and then red.

the probability is \square.
(type a fraction. simplify your answer.)

Question

if the pointer in the figure is spun twice, find the probability that the pointer lands on green and then red.

the probability is \square.
(type a fraction. simplify your answer.)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Spinner Probability", "Independent Events", "Fraction Simplification" ], "new_concepts": [], "current_concepts": [ "Spinner Probability", "Independent Events", "Fraction Simplification" ] } ## Determine individual sector probabilities $$ \begin{aligned} &P(\text{Green}) = \frac{1}{4}\ &P(\text{Red}) = \frac{1}{4}\ &P(\text{Yellow}) = \frac{1}{2} \end{aligned} $$ ## Calculate the joint probability of independent spins $$ \begin{aligned} P(\text{Green then Red}) &= P(\text{Green}) \times P(\text{Red})\ &= \frac{1}{4} \times \frac{1}{4}\ &= \frac{1}{16} \end{aligned} $$ If the pointer in the figure is spun twice, find the probability that the pointer lands on green and then red. The probability is $\frac{1}{16}$. (Type a fraction. Simplify your answer.) { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Statistics", "Spinner Probability" ] }

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Question

Explanation:

Determine individual sector probabilities

Calculate the joint probability of independent spins

Answer: