select the correct answer from each drop-down menu.

there are 10 vehicles in a parking lot: 3 suvs and 7 trucks.

the probability that any 7 randomly chosen parking spots have 2 suvs and 5 trucks or 3 suvs and 4 trucks is choose an answer. the probability that of any 7 randomly chosen vehicles, exactly 1 is an suv is choose an answer.

options for the first drop-down:
0.292
0.324
0.525
0.817

Question

select the correct answer from each drop-down menu.

there are 10 vehicles in a parking lot: 3 suvs and 7 trucks.

the probability that any 7 randomly chosen parking spots have 2 suvs and 5 trucks or 3 suvs and 4 trucks is choose an answer. the probability that of any 7 randomly chosen vehicles, exactly 1 is an suv is choose an answer.

options for the first drop-down:
0.292
0.324
0.525
0.817

Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Hypergeometric Probability", "Combinations" ], "new_concepts": [], "current_concepts": [ "Hypergeometric Probability", "Combinations" ] } ## Calculate the first probability $$ \begin{aligned} P(\text{2 SUVs, 5 trucks}) &= \frac{\binom{3}{2} \binom{7}{5}}{\binom{10}{7}} = \frac{3 \times 21}{120} = \frac{63}{120} = 0.525 \ P(\text{3 SUVs, 4 trucks}) &= \frac{\binom{3}{3} \binom{7}{4}}{\binom{10}{7}} = \frac{1 \times 35}{120} = \frac{35}{120} \approx 0.2917 \ P(\text{First Event}) &= \frac{63 + 35}{120} = \frac{98}{120} \approx 0.817 \end{aligned} $$ ## Calculate the second probability $$ \begin{aligned} P(\text{exactly 1 SUV}) &= \frac{\binom{3}{1} \binom{7}{6}}{\binom{10}{7}} = \frac{3 \times 7}{120} = \frac{21}{120} = 0.175 \end{aligned} $$ ## Question 1 The probability that any 7 randomly chosen parking spots have 2 SUVs and 5 trucks or 3 SUVs and 4 trucks is 0.817. ## Question 2 The probability that of any 7 randomly chosen vehicles, exactly 1 is an SUV is 0.175. { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Statistics", "Hypergeometric Probability" ] }

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QUESTION IMAGE

Question

Explanation:

Calculate the first probability

Calculate the second probability

Answer:

Question 1

Question 2