of the cartons produced by a company, 6% have a puncture, 7% have a smashed corner, and 0.3% have both a puncture and a smashed corner. find the probability that a randomly selected carton has a puncture or a smashed corner.

the probability that a randomly selected carton has a puncture or a smashed corner, expressed as a percentage, is %.
(type an integer or a decimal. do not round.)

Question

of the cartons produced by a company, 6% have a puncture, 7% have a smashed corner, and 0.3% have both a puncture and a smashed corner. find the probability that a randomly selected carton has a puncture or a smashed corner.

the probability that a randomly selected carton has a puncture or a smashed corner, expressed as a percentage, is  %.
(type an integer or a decimal. do not round.)

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": [ "Probability Axioms", "Compound Event" ], "new_concepts": [], "current_concepts": [ "Probability Axioms", "Compound Event", "Addition Rule for Probability" ] } ## Define events and probabilities Using the *Compound Event* knowledge point $$ \begin{aligned} &P(A) = 6\% = 0.06 \ &P(B) = 7\% = 0.07 \ &P(A \cap B) = 0.3\% = 0.003 \end{aligned} $$ ## Apply the addition rule Using the *Probability Axioms* knowledge point $$ \begin{aligned} P(A \cup B) &= P(A) + P(B) - P(A \cap B) \ &= 6\% + 7\% - 0.3\% \ &= 12.7\% \end{aligned} $$ The probability that a randomly selected carton has a puncture or a smashed corner, expressed as a percentage, is 12.7%. (Type an integer or a decimal. Do not round.) { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Statistics", "Addition Rule for Probability" ] }

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Question

Explanation:

Define events and probabilities

Apply the addition rule

Answer: