If \(X \sim B(n, p)\) and \(E(X) = 6,\ Var(X) = 4.2\), then find \(n\) and \(p\).

Q.14 If \(X \sim B(n, p)\) and \(E(X) = 6,\ Var(X) = 4.2\), then find \(n\) and \(p\).

Doubtly Asked 28 Oct 2026 Board exam · July 2025 hsc 12th Save WhatsApp Report

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Answer: \(n = 20,\ p = 0.3\)

\(E(X) = np = 6\) and \(Var(X) = npq = 4.2\). Dividing, \(q = \frac{4.2}{6} = 0.7\), so \(p = 1 - q = 0.3\).

Then \(n = \frac{6}{0.3} = 20\).

Doubtly AI · 28 Oct 2026 AI-verified · Oct 2026 Report

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