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(C) Let $E_{A}$ be the event that the sum of numbers on the dice is less than $6$. The possible outcomes for $E_{A}$ are: $E_{A} = \{(1,1), (1,2), (1,

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$\frac{1}{5}$

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(C) Let $E_{A}$ be the event that the sum of numbers on the dice is less than $6$. The possible outcomes for $E_{A}$ are: $E_{A} = \{(1,1), (1,2), (1,3), (1,4), (2,1), (2,2), (2,3), (3,1), (3,2), (4,1)\}$ Thus,$n(E_{A}) = 10$. Let $E_{B}$ be the event that the sum of numbers on the dice is $3$. The possible outcomes for $E_{B}$ are: $E_{B} = \{(1,2), (2,1)\}$ Thus,$n(E_{B}) = 2$. The required conditional probability is $P(E_{B}|E_{A}) = \frac{n(E_{B} \cap E_{A})}{n(E_{A})} = \frac{2}{10} = \frac{1}{5}$.

Two dice are thrown. If it is known that the sum of numbers on the dice was less than $6$,the probability of getting a sum as $3$ is:

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