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In a single throw of three dice, determine the probability of getting i. total of 5 ii. total of at most 5 ii. a total of at least 5. Select the correct answer from above options

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Correct Answer - (i) 1 36 (ii) 5 108 n(S)=(6×6×6)=216 (i) E1={(1,1,3),(1,3,1),(3,1,1),(1,2,2),(2,1,2),(2,2,1)} ∴P(E1)= 6 216 = 1 26 . (ii) E2={(1,1,1),(1,1,2),(1,2,1),(2,1,1),(1,1,3),(1,3,1),(3,1,1),(1,2,2),(2,1,2),(2,2,1)} E 2 = { ( 1 , 1 , 1 ) , ( 1 , 1 , 2 ) , ( 1 , 2 , 1 ) , ( 2 , 1 , 1 ) , ( 1 , 1 , 3 ) , ( 1 , 3 , 1 ) , ( 3 , 1 , 1 ) , ( 1 , 2 , 2 ) , ( 2 , 1 , 2 ) , ( 2 , 2 , 1 ) } ∴P(E2)= 10 216 = 5 108 .

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