Probability

Three urns A, B and C contain 4 red, 6 black; 5 red, 5 black; and \(\lambda\) red, 4 black balls respectively. One of the urns is selected at random and a ball is drawn. If the ball drawn is red and the probability that it is drawn from urn C is 0.4 then the square of the length of the side of the largest equilateral triangle, inscribed in the parabola \(y^2=\lambda x\) with one vertex at the vertex of the parabola, is :