an item is drawn from a box with 3 caramel chocolates, 11 dark chocolates, 9 caramel donuts, and 2 glazed donuts.
event a: chocolate
event b: caramel
$p(a \text{ or } b) = ? $
hint: $p(a \text{ or } b) = p(a) + p(b) - p(a \text{ and } b)$
round your answer to the nearest hundredth.

Question

an item is drawn from a box with 3 caramel chocolates, 11 dark chocolates, 9 caramel donuts, and 2 glazed donuts.
event a: chocolate
event b: caramel
$p(a \text{ or } b) =  ? $
hint: $p(a \text{ or } b) = p(a) + p(b) - p(a \text{ and } b)$
round your answer to the nearest hundredth.

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": [ "Theoretical Probability", "Overlapping Events" ], "new_concepts": [], "current_concepts": [ "Theoretical Probability", "Overlapping Events", "Addition Rule for Probability" ] } ## Calculate total items Using the **Theoretical Probability** knowledge point $$ \text{Total} = 3 + 11 + 9 + 2 = 25 $$ ## Find probability of Event A Using the **Theoretical Probability** knowledge point $$ \begin{aligned} &\text{Chocolates} = 3 \text{ (caramel)} + 11 \text{ (dark)} = 14\ &P(A) = \frac{14}{25} = 0.56 \end{aligned} $$ ## Find probability of Event B Using the **Theoretical Probability** knowledge point $$ \begin{aligned} &\text{Caramel items} = 3 \text{ (chocolate)} + 9 \text{ (donut)} = 12\ &P(B) = \frac{12}{25} = 0.48 \end{aligned} $$ ## Find probability of overlapping events Using the **Overlapping Events** knowledge point $$ \begin{aligned} &\text{Caramel chocolates} = 3\ &P(A \text{ and } B) = \frac{3}{25} = 0.12 \end{aligned} $$ ## Apply addition rule Using the **Overlapping Events** knowledge point $$ \begin{aligned} P(A \text{ or } B) &= P(A) + P(B) - P(A \text{ and } B)\ &= 0.56 + 0.48 - 0.12\ &= 0.92 \end{aligned} $$ An item is drawn from a box with 3 caramel chocolates, 11 dark chocolates, 9 caramel donuts, and 2 glazed donuts. Event A: chocolate Event B: caramel $P(A \text{ or } B) =$ 0.92 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Statistics", "Probability of Overlapping Events" ] }

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QUESTION IMAGE

Question

Explanation:

Calculate total items

Find probability of Event A

Find probability of Event B

Find probability of overlapping events

Apply addition rule

Answer: