a spinner has 4 numbers on it, all with an equal amount of space. the table shows the probabilities for each number. calculate the expected value.

number and probability
\begin{tabular}{|c|c|}
\hline
number & probability \\
\hline
1 & \frac{1}{4} \\
\hline
2 & \frac{1}{4} \\
\hline
3 & \frac{1}{4} \\
\hline
4 & \frac{1}{4} \\
\hline
\end{tabular}

- 1
- 3
- 2.5
- 2

Question

a spinner has 4 numbers on it, all with an equal amount of space. the table shows the probabilities for each number. calculate the expected value.

number and probability
\begin{tabular}{|c|c|}
\hline
number & probability \\
\hline
1 & \frac{1}{4} \\
\hline
2 & \frac{1}{4} \\
\hline
3 & \frac{1}{4} \\
\hline
4 & \frac{1}{4} \\
\hline
\end{tabular}

- 1
- 3
- 2.5
- 2

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Expected Value", "Probability Distribution" ], "new_concepts": [], "current_concepts": [ "Expected Value", "Probability Distribution" ] } ## Identify the values and probabilities $$ \begin{aligned} &x_1 = 1, \quad P(x_1) = \frac{1}{4} \ &x_2 = 2, \quad P(x_2) = \frac{1}{4} \ &x_3 = 3, \quad P(x_3) = \frac{1}{4} \ &x_4 = 4, \quad P(x_4) = \frac{1}{4} \end{aligned} $$ ## Apply the expected value formula $$ \begin{aligned} E(X) &= \sum_{i=1}^{4} x_i \cdot P(x_i) \ E(X) &= 1 \cdot \frac{1}{4} + 2 \cdot \frac{1}{4} + 3 \cdot \frac{1}{4} + 4 \cdot \frac{1}{4} \end{aligned} $$ ## Calculate the final sum $$ \begin{aligned} E(X) &= \frac{1 + 2 + 3 + 4}{4} \ E(X) &= \frac{10}{4} = 2.5 \end{aligned} $$

1

3

2.5

2

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Statistics", "Expected Value" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the values and probabilities

Apply the expected value formula

Calculate the final sum

Answer: