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

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

Explanation:

Define the expected value formula

$$ E(X) = \sum_{i=1}^{n} x_i \cdot P(x_i) $$

Substitute the given values from the table

$$ E(X) = 1 \cdot \frac{1}{4} + 2 \cdot \frac{1}{4} + 3 \cdot \frac{1}{4} + 4 \cdot \frac{1}{4} $$

Calculate the final sum

$$ E(X) = \frac{1 + 2 + 3 + 4}{4} = \frac{10}{4} = 2.5 $$

Answer:

\(2.5\)