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Answer: \(\dfrac{25}{216}\)

Doublets: (1,1), (2,2), ..., (6,6), i.e. 6 of the 36 outcomes, so \(p = \dfrac{6}{36} = \dfrac{1}{6}\), \(q = \dfrac{5}{6}\).

\(X\): number of successes in \(n = 4\) throws, \(X \sim B\left(4, \dfrac{1}{6}\right)\), \(P(X = x) = {}^4C_x\, p^x q^{4 - x}\).

\(P(X = 2) = {}^4C_2\left(\dfrac{1}{6}\right)^2\left(\dfrac{5}{6}\right)^2 = 6\times\dfrac{1}{36}\times\dfrac{25}{36} = \dfrac{150}{1296} = \dfrac{25}{216}\).

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