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Answer: \(P(X = 5) = \frac{3}{32}\)

Let \(X\) = number of successes in 6 throws. Odd numbers are 1, 3, 5, so \(p = \frac{3}{6} = \frac{1}{2}\) and \(q = \frac{1}{2}\). \(X \sim B\left(6, \frac{1}{2}\right)\).

\(P(X = x) = {}^6C_x \left(\frac{1}{2}\right)^x \left(\frac{1}{2}\right)^{6 - x} = {}^6C_x \left(\frac{1}{2}\right)^6\).

\(P(X = 5) = {}^6C_5 \times \frac{1}{64} = \frac{6}{64} = \frac{3}{32}\).

Doubtly AI · 29 Oct 2026 AI-generated · not yet verified Report
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