a bag contains five red marbles, two orange marbles, one yellow marble, and two green marbles. two marbles are drawn from the bag.

what is the approximate probability one of the chosen marbles is orange and one of the chosen marbles is green?

0.13333
0.02222
0.04444
0.08889

Question

a bag contains five red marbles, two orange marbles, one yellow marble, and two green marbles. two marbles are drawn from the bag.

what is the approximate probability one of the chosen marbles is orange and one of the chosen marbles is green?

0.13333
0.02222
0.04444
0.08889

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Combinations", "Classical Probability" ], "new_concepts": [], "current_concepts": [ "Combinations", "Classical Probability" ] } ## Calculate the total number of outcomes $$ \begin{aligned} \text{Total marbles} &= 5 \text{ (red)} + 2 \text{ (orange)} + 1 \text{ (yellow)} + 2 \text{ (green)} = 10 \ \text{Total ways to choose 2 marbles} &= \binom{10}{2} = \frac{10 \times 9}{2} = 45 \end{aligned} $$ ## Calculate the number of favorable outcomes $$ \begin{aligned} \text{Ways to choose 1 orange and 1 green} &= \binom{2}{1} \times \binom{2}{1} = 2 \times 2 = 4 \end{aligned} $$ ## Calculate the probability $$ \begin{aligned} P(\text{1 orange and 1 green}) &= \frac{4}{45} \approx 0.08889 \end{aligned} $$

(A) 0.13333

(B) 0.02222

(C) 0.04444

(D) 0.08889

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Statistics", "Classical Probability" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Calculate the total number of outcomes

Calculate the number of favorable outcomes

Calculate the probability

Answer: