a fruit is randomly drawn from a basket with 20 red apples, 6 green apples, 14 green pears, and 10 yellow pears.
event a: green
event b: pear
$p(a \text{ or } b) = ?$
hint: $p(a \text{ or } b) = p(a) + p(b) - p(a \text{ and } b)$
round your answer to the nearest hundredth.

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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" ] } ## Calculate total number of outcomes Using the **Theoretical Probability** knowledge point $$ \text{Total fruit} = 20 + 6 + 14 + 10 = 50 $$ ## Determine individual probabilities Using the **Theoretical Probability** knowledge point $$ \begin{aligned} P(A) &= P(\text{green}) = \frac{6 + 14}{50} = \frac{20}{50} = 0.40 \ P(B) &= P(\text{pear}) = \frac{14 + 10}{50} = \frac{24}{50} = 0.48 \end{aligned} $$ ## Determine intersection probability Using the **Theoretical Probability** knowledge point $$ P(A \text{ and } B) = P(\text{green pear}) = \frac{14}{50} = 0.28 $$ ## Apply addition rule for overlapping events Using the **Overlapping Events** knowledge point $$ \begin{aligned} P(A \text{ or } B) &= P(A) + P(B) - P(A \text{ and } B) \ P(A \text{ or } B) &= 0.40 + 0.48 - 0.28 = 0.60 \end{aligned} $$ A fruit is randomly drawn from a basket with 20 red apples, 6 green apples, 14 green pears, and 10 yellow pears. Event A: green Event B: pear $P(A \text{ or } B) =$ 0.60 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Statistics", "Overlapping Events" ] }

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Question

Explanation:

Calculate total number of outcomes

Determine individual probabilities

Determine intersection probability

Apply addition rule for overlapping events

Answer: