GATE 2022 CE (CE2) – Question 49
A pair of six-faced dice is rolled thrice. The probability that the sum of the outcomes in each roll equals 4 in exactly two of the three attempts is ______. (round off to three decimal places)
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Correct answer: 0.009 to 0.029
Explanation
A sum of four occurs as (1,3),(2,2),(3,1), so p=3/36=1/12 per independent roll. Exactly two successes among three rolls has probability $\binom32p^2(1-p)$.
This equals $33/1728=0.0190972$, rounded to **0.019**.