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Q)

Two dice are rolled. Find the probability that the sum is divisible by 2 an

Two dice are rolled. Find the probability that the sum is divisible by 2 and 3?

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A)

face of any dice can be any number from {1,2,3,4,5,6}

Hence, number of possible outcomes = 6 × 6= 36      {outcome can be any from (1,2),(1,3)..(1,6),(2,1),(2,2)...(6,6)}

Favorable outcomes are {(1,1),(1,2),(1,3),(1,5),(2,1),(2,2),(2,4),(2,6),(3,1),(3,3),(3,5),(3,6),(4,2),(4,4),(4,5),(4,6),(5,1),(5,3),(5,4),(5,5),(6,2),(6,3),(6,4),(6,6)}
(because sum of the numbers should be divisible by 2 or 3)

Number of favorable outcomes  = 24

Probability = 24/36 2/3

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