the graph on the right shows the theoretical probability of getting a given number heads in ten flips of a fair coin.

if this experiment was performed many times you would expect an average of 5 heads.

approximately, what is the probability of getting 4, 5, or 6 heads?

Question

the graph on the right shows the theoretical probability of getting a given number heads in ten flips of a fair coin.

if this experiment was performed many times you would expect an average of 5 heads.

approximately, what is the probability of getting 4, 5, or 6 heads?

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", "Probability Addition Rule", "Binomial Distribution Mean" ], "new_concepts": [ "Binomial Probability Distribution" ], "current_concepts": [ "Theoretical Probability", "Probability Addition Rule", "Binomial Distribution Mean", "Binomial Probability Distribution" ] } ## Identify individual probabilities from the graph Using the *Theoretical Probability* knowledge point $$ \begin{aligned} P(4) &\approx 0.205\ P(5) &\approx 0.246\ P(6) &\approx 0.205 \end{aligned} $$ ## Apply the addition rule for mutually exclusive events Using the *Probability Addition Rule* knowledge point $$ \begin{aligned} P(4 \text{ or } 5 \text{ or } 6) &= P(4) + P(5) + P(6)\ &= 0.205 + 0.246 + 0.205\ &= 0.656 \approx 0.66 \end{aligned} $$ Approximately, what is the probability of getting 4, 5, or 6 heads? 0.66 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Statistics", "Probability Addition Rule" ] }

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QUESTION IMAGE

Question

Explanation:

Identify individual probabilities from the graph

Apply the addition rule for mutually exclusive events

Answer: