a bag contains 3 red balls and 5 green balls.

what is the probability of picking a red ball from the bag and getting heads upon flipping a coin?

a.) $\frac{1}{8}$

b.) $\frac{3}{16}$

c.) $\frac{3}{4}$

d.) $\frac{7}{8}$

Question

a bag contains 3 red balls and 5 green balls.

what is the probability of picking a red ball from the bag and getting heads upon flipping a coin?

a.) $\frac{1}{8}$

b.) $\frac{3}{16}$

c.) $\frac{3}{4}$

d.) $\frac{7}{8}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Theoretical Probability", "Probability of Events" ], "new_concepts": [ "Independent Events Probability" ], "current_concepts": [ "Theoretical Probability", "Probability of Events", "Independent Events Probability" ] } ## Calculate the probability of picking a red ball Using the *Theoretical Probability* knowledge point $$ \begin{aligned} &\text{Total balls} = 3 + 5 = 8\ &P(\text{Red}) = \frac{3}{8} \end{aligned} $$ ## Calculate the probability of flipping heads Using the *Probability of Events* knowledge point $$ P(\text{Heads}) = \frac{1}{2} $$ ## Calculate the joint probability of both independent events Using the *Probability of Events* knowledge point $$ \begin{aligned} P(\text{Red AND Heads}) &= P(\text{Red}) \times P(\text{Heads})\ &= \frac{3}{8} \times \frac{1}{2}\ &= \frac{3}{16} \end{aligned} $$

a.) $\frac{1}{8}$

b.) $\frac{3}{16}$

c.) $\frac{3}{4}$

d.) $\frac{7}{8}$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Statistics", "Probability of Independent Events" ] }

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QUESTION IMAGE

Question

Explanation:

Calculate the probability of picking a red ball

Calculate the probability of flipping heads

Calculate the joint probability of both independent events

Answer: