# An unbiased cubic die marked with 1, 2, 2, 3, 3, 3 is rolled 3 times. The probability of getting a total score of 4 or 6 is

Question : An unbiased cubic die marked with 1, 2, 2, 3, 3, 3 is rolled 3 times. The probability of getting a total score of 4 or 6 is

(A) 16/216

(B) 50/216

(C) 60/216

(D) none of these

Solution :

Die marked with 1, 2, 2, 3, 3, 3 is throw 3 times

P(1) = 1/6, P(2) = 2/6, P(3) = 3/6

P(S) = P(4 or 6)

= P(112 (3 cases) or 123 (6 cases) or 222)

=$\ 3\times \dfrac{1}{6}\times \dfrac{1}{6}\times \dfrac{2}{6}+6\times \dfrac{1}{6}\times \dfrac{2}{6}\times \dfrac{3}{6}+\dfrac{2}{6}\times \dfrac{2}{6}\times \dfrac{2}{6}$

=$\dfrac{6+36+8}{216}=\dfrac{50}{216}$

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