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 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   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", "Discrete Random Variable" ], "new_concepts": [ "Expected Value", "Binomial Distribution Mean" ], "current_concepts": [ "Theoretical Probability", "Discrete Random Variable", "Expected Value", "Binomial Distribution Mean" ] } ## Identify the given parameters Using the *Theoretical Probability* knowledge point $$ \begin{aligned} n &= 10 \quad \text{(number of independent trials)} \ p &= 0.5 \quad \text{(probability of heads for a fair coin)} \end{aligned} $$ ## Calculate the expected value Using the *Discrete Random Variable* knowledge point $$ \begin{aligned} E[X] &= n \cdot p \ E[X] &= 10 \cdot 0.5 \ E[X] &= 5 \end{aligned} $$ 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. { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Statistics", "Expected Value" ] }

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Question

Explanation:

Identify the given parameters

Calculate the expected value

Answer: