g.pr.10.5 (mc)

a coin is tossed 3 times. you earn 5 points if there is only one head, 8 points for two heads, and 15 points for 3 heads. what is the expected number of points you would earn?

number of heads, probability and points

\begin{tabular}{|c|c|c|c|c|}
\hline
\text{number of heads} & 0 & 1 & 2 & 3 \\
\hline
\text{probability} & \frac{1}{8} & \frac{3}{8} & \frac{3}{8} & \frac{1}{8} \\
\hline
\text{points} & 0 & 5 & 8 & 15 \\
\hline
\end{tabular}

Question

g.pr.10.5 (mc)

a coin is tossed 3 times. you earn 5 points if there is only one head, 8 points for two heads, and 15 points for 3 heads. what is the expected number of points you would earn?

number of heads, probability and points

\begin{tabular}{|c|c|c|c|c|}
\hline
\text{number of heads} & 0 & 1 & 2 & 3 \\
\hline
\text{probability} & \frac{1}{8} & \frac{3}{8} & \frac{3}{8} & \frac{1}{8} \\
\hline
\text{points} & 0 & 5 & 8 & 15 \\
\hline
\end{tabular}

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Expected Value", "Probability Distribution" ], "new_concepts": [], "current_concepts": [ "Expected Value", "Probability Distribution" ] } ## Define the probability distribution of points $$ \begin{array}{c|c|c|c|c} \text{Points } (x) & 0 & 5 & 8 & 15 \ \hline \text{Probability } (P(x)) & \frac{1}{8} & \frac{3}{8} & \frac{3}{8} & \frac{1}{8} \end{array} $$ ## Calculate the expected value $$ \begin{aligned} E(X) &= \sum x \cdot P(x) \ &= 0 \cdot \frac{1}{8} + 5 \cdot \frac{3}{8} + 8 \cdot \frac{3}{8} + 15 \cdot \frac{1}{8} \ &= \frac{0 + 15 + 24 + 15}{8} \ &= \frac{54}{8} \ &= 6.75 \end{aligned} $$ $6.75$ points { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Statistics", "Expected Value" ] }

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QUESTION IMAGE

Question

Explanation:

Define the probability distribution of points

Calculate the expected value

Answer: