# Geometrical Probability includes dice?

**Discrete Mathematics**Level 3

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.