# Geometrical Probability includes dice?

Given $$a,b,c$$ are determined by throwing a dice thrice then which of the following is/are correct?

$$A)$$ the probability that origin $$(0,0)$$ lies inside the circle $$(x-a)^{2}+(y-b)^{2}=c^{2}$$ is $$\frac{1}{3}$$

$$B)$$ the probability that origin $$(0,0)$$ lies inside the circle $$(x-a)^{2}+(y-b)^{2}=c^{2}$$ is $$\frac{2}{9}$$

$$C)$$ the probability that origin $$(0,0)$$ lies on the circle $$(x-a)^{2}+(y-b)^{2}=c^{2}$$ is $$\frac{1}{108}$$

$$D)$$ the probability that origin $$(0,0)$$ lies outside the circle $$(x-a)^{2}+(y-b)^{2}=c^{2}$$ is $$\frac{82}{108}$$

Clarification: We are using an unbiased 6-sided dice. The value of $$a$$ is determine on the numerical value of the top face of the dice thrown the first time; the value of $$b$$ is determine on the numerical value of the top face of the dice thrown the second time; the value of $$c$$ is determine on the numerical value of the top face of the dice thrown the third time.

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