Consider the functions defined implicitly by the equation $$y^3-3y+x=0$$ on various intervals in the real line. If $$x\in(-\infty,-2)\cup(2,\infty)$$, the equation implicitly defines a unique real valued differentiable function $$y=f(x)$$. If $$x\in(-2,2)$$, the equation implicitly defines a unique real valued differentiable function $$y=g(x)$$ satisfying $$g(0)=0$$
$$\int\limits_{ - 1}^1 {g'\left( x \right)dx = } $$
where $$a,b,c,d$$ $$ \in \left\{ {0,1} \right\}$$
STATEMENT - 1 : The probability that the system of equations has a unique solution is $${3 \over 8}.$$ and
STATEMENT - 2 : The probability that the system of equations has a solution is $$1.$$
Let $${L_1},$$ $${L_2},$$ $${L_3}$$ be the lines of intersection of the planes $${P_2}$$ and $${P_3},$$ $${P_3}$$ and $${P_1},$$ $${P_1}$$ and $${P_2},$$ respectively.
STATEMENT - 1Z: At least two of the lines $${L_1},$$ $${L_2}$$ and $${L_3}$$ are non-parallel and
STATEMENT - 2: The three planes doe not have a common point.