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In a game of chance, a player rolls a standard six-sided die. The number rolled is the outcome of interest.
Calculate the expected value \(E(X)\) of the roll.
Interpret the result in terms of the player’s average outcome per roll.
\FieldText{1}{
Let \(X\) represent the number rolled on the die. The probability distribution of \(X\) is
\(x\)
1
2
3
4
5
6
\(P(X=x)\)
\(\frac{1}{6}\)
\(\frac{1}{6}\)
\(\frac{1}{6}\)
\(\frac{1}{6}\)
\(\frac{1}{6}\)
\(\frac{1}{6}\)
.
\(E(X) = 1 \cdot \frac{1}{6} + 2 \cdot \frac{1}{6} + 3 \cdot \frac{1}{6} + 4 \cdot \frac{1}{6} + 5 \cdot \frac{1}{6} + 6 \cdot \frac{1}{6} = 3.5\)
Since \(E(X) = 3.5\), we expect the player to roll an average of 3.5 per roll.
}
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