the diagram below represents an experiment consisting of two independent trials. find p(a and d).

$p(a \text{ and } d) = \frac{?}{}$

simplify your answer completely.

Question

the diagram below represents an experiment consisting of two independent trials. find p(a and d).

$p(a \text{ and } d) = \frac{?}{}$

simplify your answer completely.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Independent Events Probability", "Tree Diagram Multiplication" ], "current_concepts": [ "Probability Tree Diagrams", "Independent Events Probability", "Tree Diagram Multiplication" ] } ## Identify the path probabilities $$ \begin{aligned} P(A) &= \frac{2}{7} \ P(D \mid A) &= \frac{2}{3} \end{aligned} $$ ## Calculate the joint probability $$ \begin{aligned} P(A \text{ and } D) &= P(A) \times P(D \mid A) \ &= \frac{2}{7} \times \frac{2}{3} \ &= \frac{4}{21} \end{aligned} $$ The diagram below represents an experiment consisting of two independent trials. Find P(A and D). $P(A \text{ and } D) =$ $\frac{4}{21}$ Simplify your answer completely. { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Statistics", "Probability Tree Diagrams" ] }

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Question

Explanation:

Identify the path probabilities

Calculate the joint probability

Answer: