Mathematics - Probability Question with Solution | TestHub

A bag contains $N$ balls out of which 3 balls are white, 6 balls are green, and the remaining balls are blue. Assume that the balls are identical otherwise. Three balls are drawn randomly one after the other without replacement. For $i=1,2,3$, let $W_i,G_i$, and $B_i$ denote the events that the ball drawn in the $i^{\text{th }}$ draw is a white ball, green ball, and blue ball, respectively. If the probability $P\left(W_1\cap G_2\cap B_3\right)=\frac{2}{5N}$ and the conditional probability $P\left(B_3\mid W_1\cap G_2\right)=\frac{2}{9}$, then $N$ equals ________.