A pair of dice is thrown 3 times. If getting a doublet is considered a success, find the probability of two successes.

Q.6 (A) (iii) A pair of dice is thrown 3 times. If getting a doublet is considered a success, find the probability of two successes.

Doubtly Asked 29 Oct 2026 Board exam · July 2025 hsc 12th Save WhatsApp Report

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Answer: \(\frac{5}{72}\)

There are 6 doublets out of 36 outcomes, so \(p=\frac{6}{36}=\frac{1}{6}\), \(q=\frac{5}{6}\), \(n=3\). \(X\sim B\left(3,\frac{1}{6}\right)\).

\(P(X=2)={}^3C_2\,p^2q=3\times\frac{1}{36}\times\frac{5}{6}=\frac{15}{216}=\frac{5}{72}\).

Doubtly AI · 29 Oct 2026 AI-verified · Nov 2026 Report

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