Bayes theorem for defective ball

A box contains a certain number of balls out of which $80\%$ are white, $15\%$ are blue and $5\%$ are red. All the balls of the same color are indistinguishable. Among all the white balls, $\alpha\%$ are marked defective, among all the blue balls, $6\%$ are marked defective and among all the red balls, $9\%$ are marked defective. A ball is chosen at random from the box. If the conditional probability that the chosen ball is white, given that it is defective, is $0.4$, then $\alpha$ equals __________