a clothing item is randomly drawn from a box with 15 small shirts, 5 large shirts, 19 small pants, and 11 medium pants.
event a: small clothing drawn
event b: pants drawn

$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

a clothing item is randomly drawn from a box with 15 small shirts, 5 large shirts, 19 small pants, and 11 medium pants.
event a: small clothing drawn
event b: pants drawn

$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 of Probability" ] } ## Find the total number of clothing items Using the *Theoretical Probability* knowledge point $$ \text{Total items} = 15 \text{ (small shirts)} + 5 \text{ (large shirts)} + 19 \text{ (small pants)} + 11 \text{ (medium pants)} = 50 $$ ## Calculate the probability of Event A Using the *Theoretical Probability* knowledge point $$ \begin{aligned} &\text{Small items} = 15 \text{ (small shirts)} + 19 \text{ (small pants)} = 34\ &P(A) = \frac{34}{50} = 0.68 \end{aligned} $$ ## Calculate the probability of Event B Using the *Theoretical Probability* knowledge point $$ \begin{aligned} &\text{Total pants} = 19 \text{ (small pants)} + 11 \text{ (medium pants)} = 30\ &P(B) = \frac{30}{50} = 0.60 \end{aligned} $$ ## Calculate the probability of Event A and B Using the *Overlapping Events* knowledge point $$ \begin{aligned} &\text{Small pants} = 19\ &P(A \text{ and } B) = \frac{19}{50} = 0.38 \end{aligned} $$ ## Apply the addition rule for overlapping events Using the *Overlapping Events* knowledge point $$ \begin{aligned} &P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B)\ &P(A \text{ or } B) = 0.68 + 0.60 - 0.38 = 0.90 \end{aligned} $$ A clothing item is randomly drawn from a box with 15 small shirts, 5 large shirts, 19 small pants, and 11 medium pants. Event A: Small clothing drawn Event B: Pants drawn $P(A \text{ or } B) =$ 0.90 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Statistics", "Overlapping Events" ] }

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QUESTION IMAGE

Question

Explanation:

Find the total number of clothing items

Calculate the probability of Event A

Calculate the probability of Event B

Calculate the probability of Event A and B

Apply the addition rule for overlapping events

Answer: