The coefficients a, b and c of the quadratic equation, $$ax^2+bx+c=0$$ are obtained by throwing a dice three times. The probability that this equation has equal roots is

Three of the six vertices of a regular hexagon are chosen at random. The probability that the triangle with three vertices is equilateral equals

Five persons A, B, C, D and E are in queue of a shop. The probability that A and E are always together, is

If A, B and C are mutually exclusive and exhaustive events of a random experiment such that $$P(B) = {3 \over 2}P(A)$$ and $$P(C) = {1 \over 2}P(B)$$, then $$P(A \cup C)$$ equals