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Home » Thus, the probability is \(\boxed{\frac12}\). - Coaching Toolbox

Thus, the probability is \(\boxed{\frac12}\). - Coaching Toolbox

📅 May 4, 2026 👤 scraface

May 04, 2026

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Second sum ($k = 4$ to $8$):
$4\binom{8}{4} = 4 \cdot 70 = 280$
$5\binom{8}{5} = 5 \cdot 56 = 280$
$6\binom{8}{6} = 6 \cdot 28 = 168$
$7\binom{8}{7} = 7 \cdot 8 = 56$
$8\binom{8}{8} = 8 \cdot 1 = 8$
Total = $280 + 280 + 168 + 56 + 8 = 792$
Total numerator: $512 + 792 = 1304$
\mathbb{E}[\text{output}] = \frac{1304}{256} = \frac{163}{32} \approx...
Thus, the expected output is $\boxed{\dfrac{163}{32}}$.

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